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April 2019 A field-theoretic operator model and Cowen–Douglas class
Björn Gustafsson, Mihai Putinar
Banach J. Math. Anal. 13(2): 338-358 (April 2019). DOI: 10.1215/17358787-2018-0041

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.

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Björn Gustafsson. Mihai Putinar. "A field-theoretic operator model and Cowen–Douglas class." Banach J. Math. Anal. 13 (2) 338 - 358, April 2019. https://doi.org/10.1215/17358787-2018-0041

Information

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

zbMATH: 07045462
MathSciNet: MR3927877
Digital Object Identifier: 10.1215/17358787-2018-0041

Subjects:
Primary: 47B20
Secondary: 30A31, 76C05

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 2 • April 2019
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