Complex Analysis and Operator Theory

, Volume 8, Issue 6, pp 1325–1339 | Cite as

Maximal Contractive Tuples

  • B. Krishna Das
  • Jaydeb Sarkar
  • Santanu SarkarEmail author


Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\)-dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\), it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.


Contractive tuples Defect operators Defect spaces  Drury–Arveson module Fock space 

Mathematics Subject Classification (1991)

Primary 15A03 47A13 



We thank the referee for some valuable comments. The hospitality of Indian Statistical Institute, Bangalore centre is warmly and gratefully acknowledged by the first author. The third author was supported by UGC Centre for Advanced Study.


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • B. Krishna Das
    • 1
  • Jaydeb Sarkar
    • 1
  • Santanu Sarkar
    • 2
    Email author
  1. 1.Indian Statistical InstituteStatistics and Mathematics UnitBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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