Banach Journal of Mathematical Analysis

A field-theoretic operator model and Cowen–Douglas class

Björn Gustafsson and Mihai Putinar

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Abstract

In resonance with a recent geometric framework proposed by Douglas and Yang, we develop a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space. By taking advantage of the refined existing theory of the principal function of a hyponormal operator, we transfer the whole action outside the spectrum, on the resolvent of the underlying operator, localized at a distinguished vector. The whole construction turns out to rely on an elementary algebra body involving analytic multipliers and Cauchy transforms. We propose a natural field theory interpretation of the resulting resolvent functional model.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 2 (2019), 338-358.

Dates
Received: 27 June 2018
Accepted: 25 November 2018
First available in Project Euclid: 28 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1548666055

Digital Object Identifier
doi:10.1215/17358787-2018-0041

Mathematical Reviews number (MathSciNet)
MR3927877

Zentralblatt MATH identifier
07045462

Subjects
Primary: 47B20: Subnormal operators, hyponormal operators, etc.
Secondary: 30A31 76C05

Keywords
hyponormal operator exponential transform Cauchy transform ideal fluid flow

Citation

Gustafsson, Björn; Putinar, Mihai. A field-theoretic operator model and Cowen–Douglas class. Banach J. Math. Anal. 13 (2019), no. 2, 338--358. doi:10.1215/17358787-2018-0041. https://projecteuclid.org/euclid.bjma/1548666055


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References

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