%0 Journal Article
%T Diagonalization of compact operators in Hilbert modules over C*-algebras of real rank zero
%A V. M. Manuilov
%J Mathematics
%D 1995
%I arXiv
%X It is known that the classical Hilbert--Schmidt theorem can be generalized to the case of compact operators in Hilbert $A$-modules $H_A^*$ over a $W^*$-algebra of finite type, i.e. compact operators in $H_A^*$ under slight restrictions can be diagonalized over $A$. We show that if $B$ is a weakly dense $C^*$-subalgebra of real rank zero in $A$ with some additional property then the natural extension of a compact operator from $H_B$ to $H_A^*\supset H_B$ can be diagonalized with diagonal entries being from the $C^*$-algebra $B$.
%U http://arxiv.org/abs/funct-an/9501008v2