Operators, Spaces, Algebras, Modules 2010

On some classes of Hilbert C*-modules

For an element $x$ of a Hilbert C*-module $X$ we consider mappings $y\mapsto \langle x,y\rangle$ and $y\mapsto x\langle y,x\rangle.$ We present characterizations of Hilbert C*-modules over a finite-dimensional C*-algebra, and over a C*-algebra of compact operators, in terms of compactness of these mappings.