C*-Algebras over Topological Spaces: Filtrated K-Theory
نویسندگان
چکیده
منابع مشابه
C∗-algebras over Topological Spaces: Filtrated K-theory
We define the filtrated K-theory of a C∗-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences f...
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We define E-theory for separable C∗-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite approximations to this space. We obtain effective criteria for determining the invertibility of E-theory elements over possibly infinite-dimensional spaces. Fu...
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Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and s-compact. (ii) CpðXÞ is analytic. (iii) CpðXÞ is K-analytic. (iv) CpðXÞ is Lindelöf. (v) CcðX Þ is a separable metrizable and complete locally convex space. (vi) CcðX Þ is compactly dominated by irrationals. This result supplements earlier results ...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2012
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2011-061-x