1Department of Mathematical Sciences Texas A&M University College Station, TX 77843-3368, U.S.A. 2Department of Mathematics University of Missouri Columbia, MO 65201, U.S.A.
Studia Mathematica, Tome 201 (2010) no. 1, pp. 37-47
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.
Keywords:
article divided parts first linear structure set norm attaining functionals banach space prove every banach space admits infinite dimensional separable quotient equivalently renormed set norm attaining functionals contains infinite dimensional vector subspace partially solves question proposed aron gurariy second part linear structure dominated operators set dominated operators which absolutely summing lineable
Affiliations des auteurs :
Francisco Javier García-Pacheco
1
;
Daniele Puglisi
2
1
Department of Mathematical Sciences Texas A&M University College Station, TX 77843-3368, U.S.A.
2
Department of Mathematics University of Missouri Columbia, MO 65201, U.S.A.
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Francisco Javier García-Pacheco; Daniele Puglisi. Lineability of functionals and operators. Studia Mathematica, Tome 201 (2010) no. 1, pp. 37-47. doi: 10.4064/sm201-1-3
