The defect sequence for contractive tuples

Bhattacharyya, Tirthankar and Das, Bata Krishna and Sarkar, Santanu (2013) The defect sequence for contractive tuples. In: LINEAR ALGEBRA AND ITS APPLICATIONS, 438 (1). pp. 315-330.

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Abstract

We introduce the defect sequence for a contractive tuple of Hilbert space operators and investigate its properties. The defect sequence is a sequence of numbers, called defect dimensions associated with a contractive tuple. We show that there are upper bounds for the defect dimensions. The tuples for which these upper bounds are obtained, are called maximal contractive tuples. The upper bounds are different in the non-commutative and in the commutative case. We show that the creation operators on the full Fock space and the coordinate multipliers on the Drury-Arveson space are maximal. We also study pure tuples and see how the defect dimensions play a role in their irreducibility. (C) 2012 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	LINEAR ALGEBRA AND ITS APPLICATIONS
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copyright for this article belongs to ELSEVIER SCIENCE INC, NEW YORK, USA
Keywords:	Contractive tuples;Defect sequence;Defect dimensions;Maximal contractive tuples
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	31 Jan 2013 12:46
Last Modified:	31 Jan 2013 12:46
URI:	http://eprints.iisc.ac.in/id/eprint/45688

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