Extreme Flatness of Normed Modules and Arveson-wittstock Type Theorems
نویسنده
چکیده
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 in [1], and a crucial preparatory step was done in [2]. As to the monographical presentation, see the textbooks [3, 4].
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تاریخ انتشار 2008