Quaternionic Quantum q-Oscillator and Unbounded Subnormal Operators

Abstract

In this note, we observe that the class of unbounded subnormal operators on quaternionic Hilbert spaces is a solution of quaternionic q-oscillator problem whose complex case is addressed by Szefraniec in [27]. We also address the connection of unbounded subnormal operators on quaternionic Hilbert spaces, quaternionic quantum harmonic q-oscillator and quaternionic quantum Economics using model theory of unbounded subnormal operators. Moreover, we study model theory for sub-2-normal operators on quaternionic Hilbert space.

arXiv commentChanged title. Formerly " Quaternionic Quantum q-Oscillator and Unbounded Subnormal Operators in Quantum Economics". Revised version draft 14 pages, some more results included