Electronic Research Announcements

Author(s): Vladimir V. Kisil
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 26-33.
MSC (1991): Primary 46H30, 47A13; Secondary 30G35, 47A10, 47A60, 47B15, 81Q10
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Abstract: A new way of doing functional calculi is presented. A functional calculus $\Phi : f(x)\rightarrow f(T)$ is not an algebra homomorphism of a functional algebra into an operator algebra, but an intertwining operator between two representations of a group acting on the two algebras (as linear spaces). This scheme is shown on the newly developed monogenic functional calculus for an arbitrary set of non-commuting self-adjoint operators. The corresponding spectrum and spectral mapping theorem are included.

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Vladimir V. Kisil
Affiliation: Institute of Mathematics, Economics and Mechanics, Odessa State University, ul. Petra Velikogo, 2, Odessa-57, 270057, Ukraine
Email: vk@imem.odessa.ua

DOI: 10.1090/S1079-6762-96-00004-2
PII: S 1079-6762(96)00004-2
Keywords: Functional calculus, joint spectrum, group representation, intertwining operator, Clifford analysis, quantization
Received by editor(s): October 6, 1995,
Received by editor(s) in revised form: March 9, 1996
Additional Notes: This work was partially supported by the INTAS grant 93-0322. It was finished while the author enjoyed the hospitality of Universiteit Gent, Vakgroep Wiskundige Analyse, Belgium.
Communicated by: Alexandre Kirillov
Copyright of article: Copyright 1996, American Mathematical Society

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