Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unit Vectors, Morita Equivalence and Endomorphisms   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 resolve 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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat