Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Blackadar-Handelman theorem for non-unital C*-algebras   A well-known theorem of Blackadar and Handelman states that every unital
stably finite C*-algebra has a bounded quasitrace. Rather strong
generalizations of stable finiteness to the non-unital case can be obtained by
either requiring the multiplier algebra to be stably finite, or alternatively
requiring it to be at least stably not properly infinite. This paper deals with
the question whether the Blackadar-Handelman result can be extended to the
non-unital case with respect to these generalizations of stable finiteness.
  For suitably well-behaved C*-algebras there is a positive result, but none of
the non-unital versions holds in full generality. Two examples of C*-algebras
are constructed. The first one is a non-unital, stably commutative C*-algebra
$A$ that contradicts the weakest possible generalization of the
Blackadar-Handelman theorem: The multiplier algebras of all matrix algebras
over $A$ are finite, while $A$ has no bounded quasitrace. The second example is
a non-unital, simple C*-algebra $B$ that is stably non-stable, i.e. no matrix
algebra over $B$ is a stable C*-algebra. In fact, the multiplier algebras over
all matrix algebras of this C*-algebra are not properly infinite. Moreover, the
C*-algebra $B$ has no bounded quasitrace and therefore gives a simple
counterexample to a possible generalization of the Blackadar-Handelman theorem.

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th