CONTRACTIVITY AND COMPLETE CONTRACTIVITY FOR FINITE DIMENSIONAL BANACH SPACES

Misra, Gadadhar and Pal, Avijit and Varughese, Cherian (2019) CONTRACTIVITY AND COMPLETE CONTRACTIVITY FOR FINITE DIMENSIONAL BANACH SPACES. In: JOURNAL OF OPERATOR THEORY, 82 (1). pp. 23-47.

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Abstract

It is known that if m >= 3 and B is any ball in C-m with respect to some norm, say parallel to.parallel to(B), then there exists a linear map L: (C-m,parallel to.parallel to(B)*) -> M-k which is contractive but not completely contractive. The characterization of those balls in C-2 for which contractive linear maps are always completely contractive, however, remains open. We answer this question for balls of the form Omega(A) in C-2 and the balls in their norm dual, where Omega(A) = { (z(1), z(2)) : parallel to z(1) A(1) + z(2)A(2)parallel to Op < 1} for some pair of 2 x 2 matrices A(1), A(2).

Item Type:	Journal Article
Publication:	JOURNAL OF OPERATOR THEORY
Publisher:	THETA FOUNDATION
Additional Information:	Copyright of this article belongs to THETA FOUNDATION
Keywords:	Contractive and completely contractive linear maps; test functions
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	10 Feb 2020 11:40
Last Modified:	10 Feb 2020 11:40
URI:	http://eprints.iisc.ac.in/id/eprint/63336

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