This is an announcement for the paper "Operator ideals on non-commutative function spaces" by T. Oikhberg and E. Spinu.

Abstract: Suppose $X$ and $Y$ are Banach spaces, and ${\mathcal{I}}$, ${\mathcal{J}}$ are operator ideals (for instance, the ideals of strictly singular, weakly compact, or compact operators). Under what conditions does the inclusion ${\mathcal{I}}(X,Y) \subset {\mathcal{J}}(X,Y)$, or the equality ${\mathcal{I}}(X,Y) = {\mathcal{J}}(X,Y)$, hold? We examine this question when ${\mathcal{I}}, {\mathcal{J}}$ are the ideals of Dunford-Pettis, strictly (co)singular, finitely strictly singular, inessential, or (weakly) compact operators, while $X$ and $Y$ are non-commutative function spaces. Since such spaces are ordered, we also address the same questions for positive parts of such ideals.

Archive classification: math.OA

Submitted from: spinu@ualberta.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1309.5434

or

http://arXiv.org/abs/1309.5434