Rocky Mountain Journal of Mathematics

Multivariable isometries related to certain convex domains

Ameer Athavale

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Abstract

Several interesting results exist in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\mathbb{C} ^n$. We introduce a class $\Omega ^{(n)}$ of convex domains in $\mathbb{C} ^n$ which, for $n \geq 2$, is distinct from the class of strictly pseudoconvex domains and the class of bounded symmetric domains and which lends itself to the application of theories related to the abstract inner function problem and the $\overline \partial $-Neumann problem, allowing us to make a number of interesting observations about certain subnormal operator tuples associated with the members of the class $\Omega ^{(n)}$.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 1 (2018), 19-46.

Dates
First available in Project Euclid: 28 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1524880879

Digital Object Identifier
doi:10.1216/RMJ-2018-48-1-19

Mathematical Reviews number (MathSciNet)
MR3795731

Zentralblatt MATH identifier
06866698

Subjects
Primary: 47B20: Subnormal operators, hyponormal operators, etc.

Keywords
Subnormal $A$-isometry Neumann operator

Citation

Athavale, Ameer. Multivariable isometries related to certain convex domains. Rocky Mountain J. Math. 48 (2018), no. 1, 19--46. doi:10.1216/RMJ-2018-48-1-19. https://projecteuclid.org/euclid.rmjm/1524880879


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