148 research outputs found
Progress in noncommutative function theory
In this expository paper we describe the study of certain non-self-adjoint
operator algebras, the Hardy algebras, and their representation theory. We view
these algebras as algebras of (operator valued) functions on their spaces of
representations. We will show that these spaces of representations can be
parameterized as unit balls of certain -correspondences and the
functions can be viewed as Schur class operator functions on these balls. We
will provide evidence to show that the elements in these (non commutative)
Hardy algebras behave very much like bounded analytic functions and the study
of these algebras should be viewed as noncommutative function theory
Representations of B^a(E)
We present a short and elegant proof of the complete theory of strict
representations of the algebra B^a(E) of all adjointable operators on a Hilbert
B-module E by operators on a Hilbert C-module F. Aanalogue for W*-modules and
normal representations is also proved. As an application we furnish a new proof
of Blecher's Eilenberg-Watts theorem.Comment: Publication data added, corrected an ambiguity in the formulation of
Corollary 1.20 (present also in the published version) and adjusted the proof
appropriatel
Fell bundles and imprimitivity theorems
Our goal in this paper and two sequels is to apply the
Yamagami-Muhly-Williams equivalence theorem for Fell bundles over groupoids to
recover and extend all known imprimitivity theorems involving groups. Here we
extend Raeburn's symmetric imprimitivity theorem, and also, in an appendix, we
develop a number of tools for the theory of Fell bundles that have not
previously appeared in the literature.Comment: minor change
Strong Shift Equivalence of -correspondences
We define a notion of strong shift equivalence for -correspondences and
show that strong shift equivalent -correspondences have strongly Morita
equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong
shift equivalent square matrices with non-negative integer entries give stably
isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic
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