On the Intertwining of \partial{\mathcal{D}}-Isometries |
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Authors: | Ameer Athavale |
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Institution: | (1) Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India |
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Abstract: | Let be a strictly pseudoconvex bounded domain in with C
2 boundary . If a subnormal m-tuple T of Hilbert space operators has the spectral measure of its minimal normal extension N supported on , then T is referred to as a -isometry. Using some non-trivial approximation theorems in the theory of several complex variables, we establish a commutant
lifting theorem for those -isometries whose (joint) Taylor spectra are contained in a special superdomain Ω of . Further, we provide a function-theoretic characterization of those subnormal tuples whose Taylor spectra are contained in
Ω and that are quasisimilar to a certain (fixed) -isometry T (of which the multiplication tuple on the Hardy space of the unit ball in is a rather special example).
Submitted: September 9, 2007. Revised: October 10, 2007. Accepted: October 24, 2007. |
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Keywords: | " target="_blank"> Strictly pseudoconvex subnormal -isometry" target="_blank">gif" alt="$$\partial{\mathcal{D}}$$" align="middle" border="0">-isometry |
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