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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 two mentioned 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.

Copyright American Mathematical Society 1996

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Article Info

• ERA Amer. Math. Soc. 02 (1996), pp. 26-33
• Publisher Identifier: S 1079-6762(96)00004-7
• 1991 Mathematics Subject Classification. Primary 46H30, 47A13; Secondary 30G35, 47A10, 47A60, 47B15, 81Q10
• Received by the editors October 6, 1995, and, in revised form, March 9, 1996
• Communicated by Alexandre Kirillov
• Comments (When Available)

Vladimir V. Kisil

Institute of Mathematics Economics and Mechanics, Odessa State University, ul. Petra Velikogo, 2, Odessa-57, 270057, UKRAINE

E-mail address: vk@imem.odessa.ua

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.