Journal article
Operators Cauchy Dual to 2-Hyperexpansive Operators: The Multivariable Case
Integral Equations and Operator Theory, Vol.73(4), pp.481-516
08/2012
DOI: 10.1007/s00020-012-1986-4
Abstract
As a natural outgrowth of the work done in Chavan (Proc Edin Math Soc 50:637–652, 2007; Studia Math 203:129–162, 2011), we introduce an abstract framework to study generating m-tuples, and use it to analyze hypercontractivity and hyperexpansivity in several variables. These two notions encompass (joint) hyponormality and subnormality, as well as toral and spherical isometric-ness; for instance, the Drury–Arveson 2-shift is a spherical complete hyperexpansion. Our approach produces a unified theory that simultaneously covers toral and spherical hypercontractions (and hyperexpansions). As a byproduct, we arrive at a dilation theory for completely hypercontractive and completely hyperexpansive generating tuples. We can then analyze in detail the Cauchy duals of toral and spherical 2-hyperexpansive tuples. We also discuss various applications to the theory of hypercontractive and hyperexpansive tuples.
Details
- Title: Subtitle
- Operators Cauchy Dual to 2-Hyperexpansive Operators: The Multivariable Case
- Creators
- Sameer Chavan - Department of Mathematics and Statistics Indian Institute of Technology Kanpur Kanpur 208016 IndiaRaúl Curto - Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Integral Equations and Operator Theory, Vol.73(4), pp.481-516
- DOI
- 10.1007/s00020-012-1986-4
- ISSN
- 0378-620X
- eISSN
- 1420-8989
- Publisher
- SP Birkhäuser Verlag Basel; Basel
- Language
- English
- Date published
- 08/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983986095302771
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