Complex Analysis and Operator Theory

, Volume 13, Issue 1, pp 85–113 | Cite as

Deficiency Indices of Some Classes of Unbounded \(\mathbb H\)-Operators

  • B. Muraleetharan
  • K. ThirulogasantharEmail author


In this paper we define the deficiency indices of a closed symmetric right \(\mathbb H\)-linear operator and formulate a general theory of deficiency indices in a right quaternionic Hilbert space. This study provides a necessary and sufficient condition in terms of deficiency indices and in terms of S-spectrum, parallel to their complex counterparts, for a symmetric right \(\mathbb H\)-linear operators to be self-adjoint.


Quaternions Quaternionic Hilbert spaces Symmetric operator Deficiency index S-spectrum 

Mathematics Subject Classification

Primary 47B32 47S10 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JaffnaThirunelveli, JaffnaSri Lanka
  2. 2.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada

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