The standard dual of an operator space

The Dual Space of an Operator Algebra

Introduction. The purpose of this paper is to study noncommutative C*algebras as Banach spaces. The Gelfand representation of an abelian C*-algebra as the algebra of all continuous complex-valued functions on its spectrum has made it possible to apply the techniques of measure theory and the topological properties of compact Hausdorff spaces to the study of such algebras. No such structure theo...

Second dual space of little $alpha$-Lipschitz vector-valued operator algebras

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

On the fine spectra of the Zweier matrix as an operator over the weighted sequence space $l_{p}(w)$

In the present paper, the ne spectrum of the Zweier matrix as anoperator over the weighted sequence space `p(w); have been examined.

Multiplicative bijective maps on standard operator algebras

What Is an Operator Space?

These are notes for a lecture delivered on 12 May, 2008, in a graduate course on operator algebras in Berkeley. The intent was to give a brief introduction to the basic ideas of operator space theory. The notes were hastily written and have not been carefully checked for accuracy or political correctness. 1. An overview of operator spaces We learn early on that every Banach space S is isometric...