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Dilations, wandering subspaces, and inner functions

Bhattacharjee, M and Eschmeier, J and Keshari, Dinesh K and Sarkar, Jaydeb (2017) Dilations, wandering subspaces, and inner functions. In: LINEAR ALGEBRA AND ITS APPLICATIONS, 523 . pp. 263-280.

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Official URL: http://dx.doi.org/10.1016/j.laa.2017.02.032

Abstract

The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces H-K on the unit ball in C-n, wandering subspaces for restrictions of the multiplication tuple M-z = (M-z1,..,M-zn) can be described in terms of suitable H-K-inner functions. We prove that H-K-inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogeneous polynomials as an application. Along the way we prove a refinement of a result of Arveson on the uniqueness of minimal dilations of pure row contractions. (C) 2017 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: review EPrints Reviewer
Date Deposited: 25 May 2017 08:53
Last Modified: 25 May 2017 08:53
URI: http://eprints.iisc.ac.in/id/eprint/57034

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