Extreme flatness of normed modules and Arveson-Wittstock type theorems
| dc.creator | Helemskii, A. Ya. | |
| dc.date | 2008-04-09 | |
| dc.date.accessioned | 2026-07-07T09:31:17Z | |
| dc.date.available | 2026-07-07T09:31:17Z | |
| dc.description | We show in this paper that a certain class of normed modules over the algebra of all bounded operators on a Hilbert space possesses a homological property which is a kind of a functional-analytic version of the standard algebraic property of flatness. We mean the preservation, under projective tensor multiplication of modules, of the property of a given morphism to be isometric. As an application, we obtain several extension theorems for different types of modules, called Arveson-Wittstock type theorems. These, in their turn, have, as a straight corollary, the `genuine' Arveson-Wittstock Theorem in its non-matricial presentation. We recall that the latter theorem plays the role of a `quantum' version of the classical Hahn-Banach theorem on the extension of bounded linear functionals. It was originally proved by Wittstock (1981), and a crucial preparatory step was done by Arveson (1969). | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0804.1434 | |
| dc.identifier | http://arxiv.org/abs/0804.1434 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158407 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47L25; 46L07; 46M10; 46M05 | |
| dc.title | Extreme flatness of normed modules and Arveson-Wittstock type theorems | |
| dc.type | text |