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Diferenciability, renormings and analytic functions on Banach spaces - DRAFBE

Reference of the Group:

GIUV2013-021

 
Description of research activity:

The aim of the project is to study functions with smooth properties defined in Banach spaces as well as the existence of equivalent norms with "better" properties than the initial one (renormings). This study refers both to the influence that the geometric characteristics, or topological properties, of the space have on the differentiability of the norm or the existence of renormings with certain properties, and to the study of various classes of smooth functions, whether analytic, differentiable or polynomial, as Banach spaces or algebras and the operators that can be defined between them.

 
Web:

No Determinada

 
Scientific-technical goals:
  • Estudio de las propiedades de renormamiento de los espacios C(K). Calculo de formulas para conocer o estimar normas, distancias y radios espectrales
 
Research lines:
  • Renormings in Banach spaces.Study of the differentiability of functions defined on open Banach spaces, in particular of the norm.
  • Composition operators.Study of composition operators and their relationship with the properties of the symbol that defines it. Special attention to the topological properties of the operators and to the metric properties whether of the natural norm of the space or the essential one. Interest in spectral properties.
  • Infinite dimensional holomorphy.Study of the analytical applications between Banach spaces. Both their individual behaviour regarding classes of sets, as well as the possible algebraic-topological structures that they may have as a set.
 
Group members:
Name Nature of participation Entity Description
Research team
ALEJANDRO MIRALLES MONTOLIOCollaboratorUniversitat de València
 
CNAE:
  • -
 
Associated structure:
  • Mathematical Analysis
 
Keywords:
  • Espacios de Banach, diferenciabilidad Fréchet, diferenciabilidad Gâteaux, local uniformemente rotundo, rotundo, normas suaves.
  • Polinomios; funciones holomorfas; álgebras de funciones; espectro
  • BANACH SPACES
  • FRÉCHET DIFFERENTIABILITY
  • GÂTEAUX DIFFERENTIABILITY
  • UNIFORMLY ROTUND LOCAL
  • SOFT NORMS
  • COMPOSITION OPERATOR
  • STANDARD AND ESSENTIAL STANDARD
  • SPECTRA
  • POLYNOMIALS
  • HOLOMORPHIC FUNCTIONS
  • ALGEBRAS OF FUNCTIONS