Lineability of functionals and operators

Francisco Javier García-Pacheco; Daniele Puglisi

Studia Mathematica (2010)

  • Volume: 201, Issue: 1, page 37-47
  • ISSN: 0039-3223

Abstract

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This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the set of dominated operators which are not absolutely summing is lineable.

How to cite

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Francisco Javier García-Pacheco, and Daniele Puglisi. "Lineability of functionals and operators." Studia Mathematica 201.1 (2010): 37-47. <http://eudml.org/doc/285487>.

@article{FranciscoJavierGarcía2010,
abstract = {This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the set of dominated operators which are not absolutely summing is lineable.},
author = {Francisco Javier García-Pacheco, Daniele Puglisi},
journal = {Studia Mathematica},
keywords = {linear structure; norm-attaining functionals; dominated operators; lineable},
language = {eng},
number = {1},
pages = {37-47},
title = {Lineability of functionals and operators},
url = {http://eudml.org/doc/285487},
volume = {201},
year = {2010},
}

TY - JOUR
AU - Francisco Javier García-Pacheco
AU - Daniele Puglisi
TI - Lineability of functionals and operators
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 1
SP - 37
EP - 47
AB - This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the set of dominated operators which are not absolutely summing is lineable.
LA - eng
KW - linear structure; norm-attaining functionals; dominated operators; lineable
UR - http://eudml.org/doc/285487
ER -

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