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Isomorphic Submodules are Rare
by
Ronald G. Douglas
Texas A & M University
Coauthors: Jaydeb Sarkar
While Beurling's Theorem implies that each nonzero submodule of the Hardy module on the disk D is isometrically isomorphic to the Hardy module itself, a result of Richter states that for the Bergman module, the only such submodule is the Bergman module itself.
In this talk, I discuss results on this phenomenon for quasi-free Hilbert modules in the multivariate case for bounded domains in Ck showing that the phenomenon is closely related to Hardy-like modules.
Among results discussed are: (1) If the dimension of the quotient is finite, then k = 1 and only the Hardy module is possible if the domain is D. (2) If the module is essentially reductive and has an isomorphic submodule, then it is subnormal.
Date received: February 9, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-37.