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Journal of Operator Theory

Volume 59, Issue 1, Winter 2008  pp. 179-192.

Unbounded operators on Hilbert $C^*$-modules over $C^*$-algebras of compact operators

Authors Boris Guljas
Author institution: Department of Mathematics, University of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia

Summary:  The paper is devoted to closed modular densely defined operators on a Hilbert $C^*$-module $W$ over the $C^*$-algebra of compact operators on a Hilbert space. A bijective operation preserving correspondence of the set of all such operators and the set of all closed densely defined operators on a Hilbert space is obtained. The polar decomposition of a closed operator is generalized as well as some results concerning operators with compact resolvent, relative compact operators and the generalized inverse.

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