Nice Surjections on Spaces of Operators

Proceedings Mathematical Sciences

T S S R K Rao¹ 

[1] Stat-Math Unit, Indian Statistical Institute, R.V. College P.O., Bangalore 0 0, India$$

关键词: Nice surjections;    isometries;    spaces of operators.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni [9] of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on $mathcal{K}(X, Y)$ for Banach spaces 𝑋, 𝑌. We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect to other topologies on spaces of operators. We also formulate the corresponding result for $mathcal{L}(X, Y)$ thereby proving an analogue of the result from [9] for $L^p(1 < p ≠ 2 < ∞)$ spaces. We also formulate results when nice operators are not of the canonical form, extending and correcting the results from [8].

【 授权许可】

Unknown