Research of Miguel Martín

 

List of publications:
Editorial work
    Preprints submitted
    Papers
Talks
PhD students:

     

 

Field of interest:

My general research interest is in functional analysis, specially in geometry of Banach spaces.
Nowadays, my interests are concentrated on the following general areas:

 

Education:

Ph.D. in Mathematics, Universidad de Granada, Spain. 2000.

 

B.Sc. in Mathematics, Universidad de Granada, Spain. 1991 - 1996.

 

 

PhD Students:

Javier Merí, Universidad de Granada, Spain. 2006.

 

 

Editorial work:

Editor of the International Journal of Functional Analysis, Operator Theory and Applications, Pushpa publishing, ISSN: 0975-2919.

Reviewer for the Mathematical Reviews and for Zentralblatt Math.

 

 

List of Publications:

Preprints:

Polynomial numerical indices of C(K) and L_1(\mu) (with Domingo García, Bogdan Grecu, Manuel Maestre, and Javier Merí)
[November 2011]

Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces (with Vladimir Kadets)
[June 2011]

Polynomial numerical indices of Banach spaces with 1-unconditional bases (with Han Ju Lee)
[April 2011]

 

Papers:

49. Lushness, numerical index one and the Daugavet property in rearrangement invariant spaces (with Vladimir Kadets, Javier Merí and Dirk Werner), Canadian J. Math. (to appear)
[February 2011; minor changes December 2011]

48. On the numerical index of real Lp(\mu)-spaces (with Javier Merí and Mikhail Popov)
Israel J. Math. 184 (2011), 183-192.

47. Extremely non-complex Banach spaces (with Javier Merí)
Central European J. Math. 9 (2011), 797 - 802.

46. On the numerical radius of operators on Lebesgue spaces (with Javier Merí and Mikhail Popov)
J. Funct. Anal. 261 (2011), 149-168. 

45. Isometries on extremely non-complex Banach spaces (with Piotr Koszmider and Javier Merí)
J. Inst. Math. Jussieu 10 (2011), 325-348.

44. Polynomial numerical indices of Banach spaces with absolute norm (with Han Ju Lee and Javier Merí)
Linear Algebra Appl. 435 (2011), 400 - 408.

43. Numerical index of absolute sums of Banach spaces (with Javier Merí, Mikhail Popov, and Beata Randrianantoanina)
J. Math. Anal. Appl. 375 (2011), 207–222.

42. Slicely Countably Determined Banach spaces (with Antonio Avilés, Vladimir Kadets, Javier Merí, and Varvara Shepelska)
Trans. Amer. Math. Soc. 362 (2010), 4871 - 4900.

41. The polynomial Daugavet property for atomless L1(\mu)-spaces (with Javier Merí and Mikhail Popov)
Archiv der Mathematik 94 (2010), 383–389.

40. On remotality for convex sets in Banach spaces (with T. S. S. R. K. Rao)
J. Approx. Theory 162 (2010), 392-396.

39. Convexity and smoothness of Banach spaces with numerical index one (with Vladimir Kadets, Javier Merí, and Rafael Payá)
Illinois J. Math. 53 (2009), 163-182.

38. On order structure and operators in L\infty (with Irina Krasikova, Vladimir Mykhaylyuk, Javier Merí and Mikhail Popov)
Central European J. Math. 7 (2009), 683-693

37. Slicely Countably Determined Banach spaces -short note- (with Antonio Avilés, Vladimir Kadets, Javier Merí, and Varvara Shepelska)
Comptes Rendus Mathematique 347 (2009) 1277–1280

36. Lineability, spaceability, and algebrability of certain subsets of function spaces (with Francisco García-Pacheco and Juan Seoane)
Taiwanese J. Math. 13 (2009), 1257-1269.

35. Positive and negative results on the numerical index of Banach spaces and duality
Proc. Amer. Math. Soc. 137 (2009), 3067-3075.

34. Lushness, numerical index one and duality (with Vladimir Kadets, Javier Merí, and Varvara Shepelska)
J. Math. Anal. Appl. 357 (2009), 15-24.

33. Two-dimensional Banach spaces with polynomial numerical index zero (with Domingo García, Bogdan Grecu, Manuel Maestre, and Javier Merí)
Linear Algebra Appl. 430 (2009), 2488–2500

32. A note on the numerical index of the Lp space of dimension two (with Javier Merí)
Linear Multilinear Algebra 57 (2009), 201-204.

31. Properties of lush spaces and applications to Banach spaces with numerical index 1 (with Kostyantyn Boyko, Vladimir Kadets, and Javier Merí)
Studia Math. 190 (2009), 117-133.

30. Extremely non-complex C(K) spaces (with Piotr Koszmider and Javier Merí)
J. Math. Anal. Appl. 350 (2009), 601-615.

29. The polynomial numerical index for some complex vector-valued function spaces (with Yun Sung Choi, Domingo García, and Manuel Maestre)
Quart. J. Math. 59 (2008), 455-474.

28. The group of isometries of a Banach space and duality
J. Funct. Anal. 255 (2008), 2966-2976.

27. Convexity around the unit of a Banach algebra (with Vladimir Kadets, Olga Katkova, and Anna Vishnyakova)
Serdica Math. J. 34 (2008), 619-628.

26. Numerical index of Banach spaces of weakly or weakly-star continuous functions (with Ginés López and Javier Merí)
Rocky Mountain J. Math. 38 (2008), 213-223.

25. The alternative Daugavet property of C*-algebras and JB*-triples
Math. Nachr. 281 (2008), 376-385.

24. The polynomial numerical index of the real spaces c0, l1, and loo (with Sung-Guen Kim and Javier Merí)
J. Math. Anal. Appl. 337 (2008), 98-106.

23. Norm equalities for operators on Banach spaces (with Vladimir Kadets and Javier Merí)
Indiana Univ. Math. J. 56 (2007), 2385–2412.

22. Numerical index of Banach spaces and duality (with Kostyantyn Boyko, Vladimir Kadets, and Dirk Werner)
Math. Proc. Cambridge Philos. Soc. 142 (2007), 93-102.

21. The Daugavet equation for polynomials (with Yun Sung Choi, Domingo García, and Manuel Maestre)
Studia Math. 178 (2007), 63-84.

20. Numerical index of some polyhedral norms on the plane (with Javier Merí)
Linear Multilinear Algebra 55 (2007), 175-190.

19. Recent progress and open questions on the numerical index of Banach spaces (with Vladimir Kadets and Rafael Payá)
RACSAM (Rev. R. Acad. Cien. Serie A. Mat.) 100 (2006), 155–182.

18. The Daugavet property for Lindenstrauss spaces (with Julio Becerra)
in: Methods in Banach space theory (Jesus M.F. Castillo and William B. Johnson Editors), pp. 91-96,
London Mathematical Society Lecture Note Series 337, 2006.

17. On the intrinsic and the spatial numerical range (with Javier Merí and Rafael Payá)
J. Math. Anal. Appl. 318 (2006), 175-189.
An Erratum to this paper (minor changes) appears also at J. Math. Anal. Appl.

16. The Daugavet property of C*-algebras, JB*-triples, and of their isometric preduals (with Julio Becerra)
J. Funct. Anal. 224 (2005), 316 - 337

15. Finite-dimensional Banach spaces with numerical index zero (with Javier Merí and Ángel Rodríguez-Palacios)
Indiana Univ. Math. J. 53 (2004), 1279 - 1289

14. Finite-dimensional Banach spaces with numerical index zero (with Javier Merí and Ángel Rodríguez-Palacios)
Extracta Math. 19 (2004), 151 - 153

13. An alternative Daugavet Property (with Timur Oikhberg)
J. Math. Anal. Appl. 294 (2004), 158 - 180

12. On CL-spaces and almost-CL-spaces (with Rafael Payá)
Arkiv Mat. 42 (2004), 107 - 118

11. The daugavetian index of a Banach space
Taiwanisse J. Math. 7 (2003), 631 - 640

10. Numerical index and Daugavet property for $L_\infty(\mu,X)$ (with Armando R. Villena)
Proc. Edinburgh Math. Soc. 46 (2003), 415 - 420

9. Banach spaces having the RNP and numerical index 1
 Proc. Amer. Math. Soc. 131 (2003), 3407 - 3410

8. Structure of nested sequences of balls in Banach spaces (with P. Bandyopadhyay, V. P. Fonf and B.-L. Lin)
Houston J. Math. 29 (2003), 173 - 193.

7. Numerical index and renorming (with Catherine Finet and Rafael Payá)
Proc. Amer. Math. Soc. 131 (2003), 871 - 877

6. Some recent results on the numerical index of a Banach space
Publicaciones Matemáticas de la Universidad Complutense de Madrid (Colloquium), 49, pp. 49 - 54, 2002

5. The alternative Dunford-Pettis property in the predual of a von Neumann algebra (with Antonio M. Peralta)
Studia Math. 147 (2001), 197 - 200

4. Indice numerico y subespacios (spanish)
Actas del ‘Encuentro de Matematicos andaluces’, (Sevilla, November 13-17, 2000), vol. 2, pp. 641 - 648, 2001

3. Numerical index of vector-valued function spaces (with Rafael Payá)
Studia Math. 142 (2000), 269 - 280

2. A survey on the numerical index of a Banach space
 Extracta Math. 15 (2000), 265 - 276

1. Real Banach spaces with numerical index 1 (with Ginés López and Rafael Payá)
Bull. London Math. Soc. 31 (1999), 207 - 212

 

Some Talks:

Here you can find a list of my talks, some of them with the slides.

“¡Hasta el infinito y más allá!" (Spanish), XI Semana de la Ciencia, Facultad de Ciencias, Universidad de Granada, Granada (Spain), November 2011.

“Isometrías de un espacio de Banach y dualidad" (Spanish), Seminario de Análisis y Aplicaciones, UAM-ICMAT, Madrid (Spain), November 2011.

“¿Dónde está el infinito?" (Spanish), Facultad de Matemáticas, Universidad de Valencia, Valencia (Spain), September 2011.

“Un ejemplo de comportamiento extremo del grupo de las Isometrías de un espacio de Banach respecto a la dualidad” (Spanish), Seminario del Departamento de Análisis Matemático,
Universidad de Valencia, Valencia (Spain), September 2011.

“Isometries of Banach spaces and duality”, City College of New York (CUNY). New York (USA), July 2011.

“On the numerical radius of operators on Lebesgue spaces”, Pohang Mathematics Institute, POSTECH, Pohang (Korea), March 2011.

“About the mathematical infinity”, Dongguk University,
Seoul (Korea), March 2011.

“On the numerical radius of operators on Lebesgue spaces”, i-Math Consolider Trimester on Functional Analysis, Complex Analysis and Operator Theory, Universidad Politécnica de Valencia,
Valencia (Spain), February 2011.

“Slicely Countably Determined Banach spaces”, Seminario Rey Pastor, Universidad de Murcia,
Murcia (Spain), December 2010.

“Numerical ranges and numerical indices”, a series of 3 lectures at the 1st ILJU School of Mathematics - Functional Analyisis -,
Pohang Mathematics Institute, Yong Pyong resort, Pyeongchang (Korea), August 2009.

“Slicely Countably Determined Banach spaces”, I Encuentro SMM - RSME, Oaxaca (Mexico), July 2009.

“The Daugavet property ”, Indian Statistical Institute, Kolkata centre, Kolkata (India), June 2009.

“Numerical index theory”, a series of 8 lectures at the Workshop on Geometry of Banach spaces and its Applications,
Indian Statistical Institute Bangalore center, Bangalore (India), June 2009.
* The full version of the talk (with all proofs) is here. Course notes are available here.

“Slicely Countably Determined Banach spaces”, Colloquium del Departamento de Análisis Matemático,
Universidad Complutense de Madrid, Madrid (Spain), May 2009.

“The numerical index of Banach spaces”, Seminario Rubio de Francia, Universidad de Zaragoza,
Zaragoza (Spain), April 2009.

“Isometries on extremely non-complex Banach spaces”, a series of 3 lectures at the 37 Winter School in Abstract Analysis,
Kacov (Czech Republic), January 2009.

“Isometrías de un espacio de Banach y dualidad” (Spanish), Seminario del Departamento de Análisis Matemático,
Universidad de Granada, Granada (Spain), January 2009.

“Slicely Countably Determined Banach spaces”, Workshop in Analysis and Probability,
Texas A&M University, College Station, TX (USA), August 2008.

“Extremely non-complex C(K) spaces ”, Second International Conference in Set Theory, Topology and Banach Spaces,
Kielce (Poland), July 2008.

“The numerical index of a Banach space”, IV Encuentro de Análisis Funcional Murcia-Valencia ,
Alcoy, Alicante (Spain), May 2008.

“Isometrías de un espacio de Banach y dualidad”, Seminario de Análisis Funcional, Departamento de Matemáticas,
Universidad de Murcia, Murcia (Spain), February 2008.

“Igualdades de normas para operadores y rango numérico. Prehistoria, historia y resultados recientes” (Spanish-English), Curso Avanzado del Departamento de Análisis Matemático de la Universidad de Valencia,
 Valencia (Spain), December 2007.

“On a C(K) space with few operators”, 22nd summer conference on Topology and its Applications,
 Castellón (Spain), July 2007.

“The groups of isometries of a Banach space and duality”, First French-Spanish Congress of Mathematics,
Zaragoza (Spain), July 2007.

“The Daugavet property for polynomials ”, Banach space theory: classical topics and new directions,
Cáceres (Spain), September 2006.

“Numerical index of Banach spaces and duality”, ICM2006, Madrid (Spain), August 2006.

“Norm equalities for operators”, Poster presented by Javier Merí,
awarded with the 1st prize of the Poster competition at the ICM2006 (section 9),Madrid (Spain), August 2006.

“The Daugavet property ”, Seminario de Análisis Matemático,
Universidad de Sevilla (Spain), June 2006.

“Norm equalities for operators”, III Workshop on Functional Analysis,
La Manga del Mar Menor, Murcia (Spain), March 2006.

“Norm equalities for operators in the spirit of Daugavet equation ”, Faot2005,
Mondello, Palermo (Italy), September 2005.

“Numerical index of Banach spaces and duality”, IVth International Workshop on Functional Analysis
on the occasion of the 65th birthday of Jean Schmets, Liege (Belgium), September 2005.

“The alternative Daugavet property”, Fachbereich Mathematik und Informatik,
Freie Universität Berlin (Germany), May 2005.

“The Daugavet property for C*-algebras and von Neumann preduals”, Séminaire d'Initiation à l'Analyse,
Equipe d'Analyse Fonctionnelle, Université Pierre et Marie Curie - Paris 6 (France), May 2005.

“La propiedad de Daugavet” (Spanish), Departamento de Análisis Matemático,
Universidad Complutense de Madrid (Spain), March 2005.

“The Daugavet property”, Colloquium of the Math. Department,
Kent State University, Kent, OH (USA), February 2005.

“The Daugavet property in C*-algebras and von Neumann preduals”, V Conference on Banach spaces,
Caceres (Spain), September 2004

“Geometric characterizations of the Daugavet property in C*-algebras and von Neumann preduals”,
Functional Analysis Workshop, Joensuu (Finland), June 2004

“Índice numérico de los espacios de Banach” (spanish), Seminario del Departamento de Análisis Matemático,
Universitat de Valencia (Spain), May 2004

“La propiedad de Daugavet” (spanish), Seminario del Departamento de Análisis Matemático,
Universitat de Valencia (Spain), September 2003

“Finite-dimensional Banach spaces with numerical index zero”, SUMIRFAS,
Texas A&M University, College Station, TX (USA), July 2003

“CL-spaces and almost-CL-spaces”, The Wladylaw Orlicz Conference and Function Spaces VII,
Poznan (Poland), July 2003

“Existence of hermitian operators on finite-dimensional Banach spaces: geometrical consecuences”,
First Join Meeting RSME-AMS, Sevilla (Spain), June 2003

“The numerical index of a Banach space”, Seminar of the Department of Mathematics,
 University of California, Irvine (USA), November 2001

“An alternative Daugavet Property”, 2001 Fall Western Section Meeting (meeting #972),
American Mathematical Society, Irvine, California (USA), November 2001

“La propiedad de Daugavet” (spanish), Seminario del Departamento de Matemáticas,
Universidad Autonoma de Madrid (Spain), September 2001

“Algunas cuestiones sobre Indice numerico” (spanish), Colloquium del Departamento de Análisis Matemático,
Universidad Complutense de Madrid (Spain), September 2001

“Indice numerico y subespacios” (spanish), Encuentro de Matemáticos Andaluces,
Universidad de Sevilla (Spain), November 2000

“Renorming and numerical index of Banach spaces”, Summer school ‘Functional Analysis’,
Universite de Franche-Comte, Besançon (France), June 2000

“The numerical index of Banach spaces”, Seminar of the Department of Mathematics and Computer Sciences,
University of Iowa (USA), March and April, 2000

“What’s the matter if a Banach space has numerical index 1?”, Seminar of the Department of Mathematics,
University College Dublin (Ireland), August 1999

“Espacios de Banach reales con indice numerico uno” (spanish), III Congress on Banach spaces,
Universidad de Extremadura (Spain), November 1998

“Espacios de Banach con indice numerico uno” (spanish), Espacios de Banach,
Cursos de verano de Laredo, Universidad de Cantabria (Spain), August 1997


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