Article ID Journal Published Year Pages File Type
6416719 Linear Algebra and its Applications 2013 16 Pages PDF
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 co-ordinate 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.

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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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