Diagonalization of compact operators in Hilbert modules over C-algebras of real rank zero
نویسنده
چکیده
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 HB to H∗ A ⊃ HB can be diagonalized with diagonal entries being from the C∗-algebra B.
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