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arXiv · 1709.08547

A Toolkit for Constructing Dilations on Banach Spaces

Stephan Fackler·Jochen Glück
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Abstract

We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if $X$ is a super-reflexive Banach space and $T$ is contained in the weakly closed convex hull of all invertible isometries on $X$, then $T$ admits a dilation to an invertible isometry on a Banach space $Y$ with the same regularity as $X$. The classical dilation theorems of Sz.-Nagy and Akcoglu-Sucheston are easy consequences of our general theory.

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BibTeXRIS

Stephan Fackler, Jochen Glück. 2017-09-25. A Toolkit for Constructing Dilations on Banach Spaces. https://doi.org/10.1112/plms.12201

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