Linearly isomorphic structures and isometric structures in Banach spaces

• Grant number: 10/17493-1
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2011
• End date: February 28, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Valentin Raphael Henri Ferenczi
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In the two years 2011-2012, several directions of research will be explored in general Banach space theory. The first direction is the direction of Gowers' list in Banach spaces, where the objective is the classification of Banach spaces up to isomorphism, in function of the type of subspaces they contain. The second direction is the study of isometry groups in Banach, where is studied the relation between the isomorhpic structure of a Banach space $X$ and the structure of the isometry group on $X$ in any equivalent norm, in relation with Mazur's rotations problem and associated questions. The third direction is the study of complex structures on real Banach spaces, where the uniqueness of such structures is studied in relation to the existence of an unconditional basis in the space. Finally, the fourth direction is the direction of geometry of Banach spaces and complexity, where is studied how many non isomorphic subspaces must a Banach space contain, as well as cases of homogeneity, in relation with Gowers homogeneous space theorem. Part of the project are participations of the candidate in conferences or collaborations abroad, and two visits of foreign professors in Brazil in 2011 and 2012. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FERENCZI, V.; SCHLUMPRECHT, TH.. Subsequential minimality in Gowers and Maurey spaces. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, v. 106, n. 1, p. 163-202, JAN 2013. (10/17493-1)

FERENCZI, VALENTIN; ROSENDAL, CHRISTIAN. ON ISOMETRY GROUPS AND MAXIMAL SYMMETRY. Duke Mathematical Journal, v. 162, n. 10, p. 1771-1831, JUL 15 2013. (10/05182-1, 10/17493-1)

FERENCZI, V.; SCHLUMPRECHT, TH.. Subsequential minimality in Gowers and Maurey spaces. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, v. 106, p. 40-pg., 2013-01-01. (10/17493-1)