Unit Vectors, Morita Equivalence and Endomorphisms
Michael Skeide
Source: Publ. Res. Inst. Math. Sci. Volume 45, Number 2 (2009), 475-518.
Abstract
We solve two problems in the theory of correspondences that have important implications in the theory of product systems. The first problem is the question whether every correspondence is the correspondence associated (by the representation theory) with a unital endomorphism of the algebra of all adjointable operators on a Hilbert module. The second problem is the question whether every correspondence allows for a nondegenerate faithful representation on a Hilbert space. We also solve an extension problem for representations of correspondences and we provide new efficient proofs of several well-known statements in the theory of representations of W$^∗$–algebras.
Primary Subjects: 46L55, 46L53, 60J25, 46L08
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.prims/1241553127
Digital Object Identifier: doi:10.2977/prims/1241553127
Mathematical Reviews number (MathSciNet):
MR2510509
Zentralblatt MATH identifier:
05591480
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