Measures of noncompactness on the standard Hilbert C^*-module

2017/11/26 by Kečkić, Dragoljub J., Lazović, Zlatko
#54E15 #FOS: Mathematics #Operator Algebras (math.OA) #Primary: 46L08 #Secondary: 47H08

paper · doi:10.48550/arxiv.1711.09466

Abstract

We define a measure of noncompactness λ on the standard Hilbert C^*-module l²(\mathcal A) over a unital C^*-algebra, such that λ(E)=0 if and only if E is \mathcal A-precompact (i.e. it is ε-close to a finitely generated projective submodule for any ε>0) and derive its properties. Further, we consider the known, Kuratowski, Hausdorff and Istrăţescu measure of noncomapctnes on l²(\mathcal 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 λ.

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