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In this paper we define the quaternionic Cayley transformation of a denselydefined, symmetric, quaternionic right linear operator and formulate a generaltheory of defect number in a right quaternionic Hilbert space. This studyinvestigates the relation between the defect number and S-spectrum, and theproperties of the Cayley transform in the quaternionic setting.

S-Spectrum and the quaternionic Cayley transform of an operator