Compact separating maps on continuous fields of Banach spaces

Separating Linear Maps of Continuous Fields of Banach Spaces∗

Compact operators on Banach spaces

In this note I prove several things about compact linear operators from one Banach space to another, especially from a Banach space to itself. Some of these may things be simpler to prove for compact operators on a Hilbert space, but since often in analysis we deal with compact operators from one Banach space to another, such as from a Sobolev space to an L space, and since the proofs here are ...

Banach module valued separating maps and automatic continuity

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

On Weakly Compact Subsets of Banach Spaces

Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...

Compact operators on Banach spaces: Fredholm-Riesz

1. Compact operators on Banach spaces 2. Appendix: total boundedness and Arzela-Ascoli [Fredholm 1900/1903] treated compact operators as limiting cases of finite-rank operators. [1] [Riesz 1917] defined and made direct use of the compactness condition, more apt for Banach spaces. See [Riesz-Nagy 1952] for extensive discussion in the Hilbert-space situation, and many references to original paper...