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Some Non-linear Geometrical Properties of Banach Spaces

  • Domingo García
  • Manuel MaestreEmail author
Conference paper
  • 1.1k Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 80)

Abstract

In this survey we report on very recent results about some non-linear geometrical properties of many classes of real and complex Banach spaces and uniform algebras, including the ball algebra \(\fancyscript{A}_u(B_X)\) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space \(X\). These geometrical properties are: Polynomial numerical index, Polynomial Daugavet property and Bishop-Phelp-Bollobás property for multilinear mappings.

Keywords

Disk algebra Numerical index Daugavet property  Banach space 

Notes

Acknowledgments

The authors were supported by MICINN Project MTM2011-22417 and Prometeo II/2013/013.

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Departamento de Análisis MatemáticoUniversidad de ValenciaBurjasot (Valencia)Spain

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