Reflexive operator algebras on Banach spaces

Q-reflexive Banach Spaces

Let E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...

Local Automorphisms of Operator Algebras on Banach Spaces

In this paper we extend a result of Šemrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms ...

Exponentiation of Operator Lie Algebras on Banach Spaces

On Polar Cones and Differentiability in Reflexive Banach Spaces

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

Spatiality of Derivations of Operator Algebras in Banach Spaces

and Applied Analysis 3 The role of “compact operators” is replaced by that of “minimal one-sided ideals”. The proof of our results relies on the quasispatiality of the derivation and Banach algebra techniques. This paper is a continuation of 5 . Some definitions and notations can be found in 5 . 2. Preliminaries Throughout this paper, X is a complex Banach space, and X∗ is the topological dual ...