The defect sequence for contractive tuples

Bhattacharyya, Tirthankar ; Das, Bata Krishna ; Sarkar, Santanu (2013) The defect sequence for contractive tuples Linear Algebra and its Applications, 438 (1). pp. 315-330. ISSN 0024-3795

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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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Contractive Tuples; Defect Sequence; Defect Dimensions; Maximal Contractive Tuples
ID Code:99731
Deposited On:27 Nov 2016 12:51
Last Modified:27 Nov 2016 12:51

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