Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable isomorphism and strong Morita equivalence of operator algebras   We introduce a Morita type equivalence: two operator algebras $A$ and $B$ are
called strongly $\Delta $-equivalent if they have completely isometric
representations $\alpha $ and $\beta $ respectively and there exists a ternary
ring of operators $M$ such that $\alpha (A)$ (resp. $\beta (B)$) is equal to
the norm closure of the linear span of the set $M^*\beta (B)M, $ (resp.
$M\alpha (A)M^*$). We study the properties of this equivalence. We prove that
if two operator algebras $A$ and $B,$ possessing countable approximate
identities, are strongly $\Delta $-equivalent, then the operator algebras
$A\otimes \cl K$ and $B\otimes \cl K$ are isomorphic. Here $\cl K$ is the set
of compact operators on an infinite dimensional separable Hilbert space and
$\otimes $ is the spatial tensor product. Conversely, if $A\otimes \cl K$ and
$B\otimes \cl K$ are isomorphic and $A, B$ possess contractive approximate
identities then $A$ and $B$ are strongly $\Delta $-equivalent.

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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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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: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th