F. Galaz-Fontes (Proc. AMS., 1998) has established a criterion for a subset of the space of compact linear operators from a reflexive and separable space X into a Banach space Y to be compact. F. Mayoral (Proc. AMS., 2000) has extended this criterion to the case of Banach spaces not containing a copy of l^1 . The purpose of this note is to give a new proof of the result of F. Mayoral. In our proof, we use l^∞ -spaces, a well known result of H. P. Rosenthal and L.E. Dor which characterizes the spaces without a copy of l^1 and a recent result obtained by G. Nagy in 2007 concerining compact sets in normed spaces. We point out that another proof of Mayoral’s result was given by E. Serrano, C. Pineiro and J.M. Delgado (Proc. AMS., 2006)...
This note presents several observations on Banach spaces X such that, for fixed $1 ≤ p ≤ ∈fty$, eve...
We consider the question: is every compact set in a Banach space X contained in the closed unit rang...
We consider the question: is every compact set in a Banach space X contained in the closed unit rang...
AbstractWe prove that there is a bounded linear operator T: l∞ → l∞ for which there is no closest co...
summary:In the first part of the paper we prove some new result improving all those already known ab...
summary:In the first part of the paper we prove some new result improving all those already known ab...
AbstractWe show that there is no surjective compact operator on a normed linear infinite-dimensional...
AbstractLet E and F be Banach spaces. We generalize several known results concerning the nature of t...
AbstractThe main result is that every weakly compact operator between Banach spaces factors through ...
AbstractLet E and F be Banach spaces. We generalize several known results concerning the nature of t...
. We present a new simple proof that if a relatively weakly compact subset of L1 satisfies the Bocce...
AbstractLet X be a Banach space. Then there is a locally convex topology for X, the “Right topology,...
For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions ...
In this note we revise and survey some recent results established in [8]. We shall show that for eac...
AbstractWe prove that weakly compact operators on a non-reflexive normed space cannot be bijective. ...
This note presents several observations on Banach spaces X such that, for fixed $1 ≤ p ≤ ∈fty$, eve...
We consider the question: is every compact set in a Banach space X contained in the closed unit rang...
We consider the question: is every compact set in a Banach space X contained in the closed unit rang...
AbstractWe prove that there is a bounded linear operator T: l∞ → l∞ for which there is no closest co...
summary:In the first part of the paper we prove some new result improving all those already known ab...
summary:In the first part of the paper we prove some new result improving all those already known ab...
AbstractWe show that there is no surjective compact operator on a normed linear infinite-dimensional...
AbstractLet E and F be Banach spaces. We generalize several known results concerning the nature of t...
AbstractThe main result is that every weakly compact operator between Banach spaces factors through ...
AbstractLet E and F be Banach spaces. We generalize several known results concerning the nature of t...
. We present a new simple proof that if a relatively weakly compact subset of L1 satisfies the Bocce...
AbstractLet X be a Banach space. Then there is a locally convex topology for X, the “Right topology,...
For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions ...
In this note we revise and survey some recent results established in [8]. We shall show that for eac...
AbstractWe prove that weakly compact operators on a non-reflexive normed space cannot be bijective. ...
This note presents several observations on Banach spaces X such that, for fixed $1 ≤ p ≤ ∈fty$, eve...
We consider the question: is every compact set in a Banach space X contained in the closed unit rang...
We consider the question: is every compact set in a Banach space X contained in the closed unit rang...