Measures of noncompactness on the standard hilbert C*-module
Copyright policy )Measures of noncompactness on the standard hilbert C*-module
We define a measure of noncompactness ? on the standard Hilbert C*-module l2(A) over a unital C*-algebra, such that ?(E) = 0 if and only if E is A-precompact (i.e. it is ?-close to a finitely generated projective submodule for any ? > 0) and derive its properties. Further, we consider the known, Kuratowski, Hausdorff and Istr??escu measure of noncompactnes on l2(A) regarded as a locally convex space with respect to a suitable topology, and obtain their properties as well as some relationship between them and introduced measure of noncompactness ?.
- University of Belgrade Serbia
\(C^*\)-modules, uniform spaces, Uniform structures and generalizations, Mathematics - Operator Algebras, FOS: Mathematics, Hilbert module, Primary: 46L08, Secondary: 47H08, 54E15, Operator Algebras (math.OA), Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc., measures of noncompactness
\(C^*\)-modules, uniform spaces, Uniform structures and generalizations, Mathematics - Operator Algebras, FOS: Mathematics, Hilbert module, Primary: 46L08, Secondary: 47H08, 54E15, Operator Algebras (math.OA), Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc., measures of noncompactness
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