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arXiv · 1512.08662

Deficiency Indices of Some Classes of Unbounded $\mathbb{H}$-Operators

B. Muraleetharan·K. Thirulogasanthar
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Abstract

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.

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B. Muraleetharan, K. Thirulogasanthar. 2017-09-08. Deficiency Indices of Some Classes of Unbounded $\mathbb{H}$-Operators. https://doi.org/10.1007/s11785-017-0702-4

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