Measures of noncompactness on the standard Hilbert C*-module

الأصل · EN

We define a measure of noncompactness λ on the standard Hilbert C*-module l²(A) over a unital C*-algebra, such that λ(E)=0 if and only if E is 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(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.