The defect sequence for contractive tuples

详细信息    查看全文

• 作者：Tirthankar Bhattacharyya^a ; ^{tirtha@math.iisc.ernet.in} ; Bata Krishna Das^b ; ^{b.das@lancaster.ac.uk} ; Santanu Sarkar^a ; ^{santanu@math.iisc.ernet.in}
• 关键词：Primary ; 46L07 ; Secondary ; 46L08 ; 46E22 ; 46B20
• 刊名：Linear Algebra and its Applications
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：438
• 期：1
• 页码：315-330
• 全文大小：307 K

文摘

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.