Nonmatricial Version of the Arveson–Wittstock Extension Principle, and Its Generalization

A. Ya. Helemskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We consider the algebra $\mathcal{B}=\mathcal{B}(H)$ of bounded operators in a Hilbert space $H$, $\mathcal{B}$-bimodules, and morphisms of these bimodules into the algebra $\mathcal{B}(L\otimes H)$, where $L$ is a Hilbert space. We study the problem of extension of a morphism defined on a sub-$\mathcal{B}$-bimodule $Y\subset Z$ to $Z$. This problem is solved for Ruan bimodules.

Keywords: Ruan bimodule, bimodule tensor product, q-norm, q-space, completely bounded operator, Arveson–Wittstock theorem.

UDC: 517.98+512.664.1

Received: 19.02.2007

DOI: 10.4213/faa2913

 English version: Functional Analysis and Its Applications, 2008, 42:3, 213–219

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