Journal of Operator Theory

Volume 53, Issue 1, Winter 2005 pp. 169-184.

Hilbert-Schmidt submodules and issues of unitary equivalence

Authors: Rongwei Yang
Author institution: Department of Mathematics and Statistics, SUNY at Albany, Albany, NY 12222, USA

Summary: The first half of this paper studies the {\em $M_q$-type} submodules over the bidisk. Because of their structural simplicity, $M_q$-type submodules are used to address several issues regarding the unitary equivalence of submodules. $M_q$-type submodules lie inside a much bigger class --- the class of {\em Hilbert-Schmidt submodules} which we will define in the second half of the paper. Several facts are put in place to raise two conjectures about Hilbert-Schmidt submodules. The Hilbert-Schmidt submodule possesses a numerical invariant which is a natural analogue of Arveson's curvature invariant over the unit ball.

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