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Operator positivity and analytic models of commuting tuples of operators

Bhattacharjee, Monojit and Sarkar, Jaydeb (2016) Operator positivity and analytic models of commuting tuples of operators. In: STUDIA MATHEMATICA, 232 (2). pp. 155-171.

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Official URL: http://dx.doi.org/10.1016/j.jallcom.2016.03.260

Abstract

We study analytic models of operators of class C-.0 with natural positivity assumptions. In particular, we prove that for an m-hypercontraction T is an element of C-.0 on a Hilbert space H, there exist Hilbert spaces epsilon and epsilon(*) and a partially isometric multiplier theta is an element of M(H-2 (epsilon), A(m)(2) (epsilon(*))) such that H congruent to Q(theta) - A(m)(2) (epsilon*) circle minus theta H-2(epsilon) and P-Q theta M-z vertical bar Q(theta), where A(m)(2) (epsilon(*)) is the epsilon(*)-valued weighted Bergman space and H-2 (epsilon) is the E-valued Hardy space over the unit disc a We then proceed to study analytic models for doubly commuting n-tuples of operators and investigate their applications to joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over the polydisc. In particular, we completely analyze doubly commuting quotient modules of a large class of reproducing kernel Hilbert modules, in the sense of Arazy and Englis, over the unit polydisc D-n.

Item Type: Journal Article
Additional Information: ELSEVIER SCIENCE SA, PO BOX 564, 1001 LAUSANNE, SWITZERLAND
Keywords: weighted Bergman spaces; hypercontractions; multipliers; reproducing kernel Hilbert spaces; invariant subspaces
Department/Centre: Division of Chemical Sciences > Materials Research Centre
Depositing User: Id for Latest eprints
Date Deposited: 10 Jun 2016 05:28
Last Modified: 10 Jun 2016 05:28
URI: http://eprints.iisc.ac.in/id/eprint/53991

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