Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 11, Number 5 (2005), 739-757.
Monogenic Calculus as an Intertwining Operator
We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint (n\times n) matrices.
Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 5 (2005), 739-757.
First available in Project Euclid: 7 March 2005
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47A60: Functional calculus 30G35: Functions of hypercomplex variables and generalized variables 46H30: Functional calculus in topological algebras [See also 47A60] 47A10: Spectrum, resolvent 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
Kisil, Vladimir V. Monogenic Calculus as an Intertwining Operator. Bull. Belg. Math. Soc. Simon Stevin 11 (2005), no. 5, 739--757. https://projecteuclid.org/euclid.bbms/1110205630.