Lineability of functionals and operators

• Autorzy: Francisco Javier García-Pacheco , Daniele Puglisi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 201
• Numer: 1
• Strony: 37-47

Daty

wydano

2010

Twórcy

autor

Francisco Javier García-Pacheco

• Department of Mathematical Sciences, Texas A&M University, College Station, TX 77843-3368, U.S.A.

autor

Daniele Puglisi

• Department of Mathematics, University of Missouri, Columbia, MO 65201, U.S.A.

Identyfikatory

DOI

10.4064/sm201-1-3