Lineability of functionals and operators
Volume 201 / 2010
Studia Mathematica 201 (2010), 37-47
MSC: Primary 46B03; Secondary 47B38.
DOI: 10.4064/sm201-1-3
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.
