Deficiency Indices of Some Classes of Unbounded \(\mathbb H\)-Operators
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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.
KeywordsQuaternions Quaternionic Hilbert spaces Symmetric operator Deficiency index S-spectrum
Mathematics Subject ClassificationPrimary 47B32 47S10
- 3.Alpay, D., Colombo, F., Kimsey D.P.: The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum. J. Math. Phys. 57, 023503 (2016)Google Scholar