(DN)-(Ω)-type conditions for Fréchet operator spaces

Krzysztof Piszczek

Vol. 261 (2013), No. 1, 237–256

DOI: 10.2140/pjm.2013.261.237

Abstract

We introduce (DN)-(Ω)-type conditions for Fréchet operator spaces. We investigate which quantizations carry over the above conditions from the underlying Fréchet space onto the operator space structure. This holds in particular for the minimal and maximal quantizations in case of a Fréchet space and — additionally — for the row, column and Pisier quantizations in case of a Fréchet–Hilbert space. We also reformulate these conditions in the language of matrix polars.

Keywords

operator space, Fréchet space, (DN)-(Ω)-type conditions, quantization

Mathematical Subject Classification 2010

Primary: 46A13, 46A32, 46A63, 47L25

Secondary: 46M05, 46A45

Milestones

Received: 13 December 2011

Accepted: 27 September 2012

Published: 28 February 2013