Abstract
In this chapter we will extend functional calculus to families of commuting self-adjoint operators. As an application of this extension we will be able to introduce in Sect. 7.4 functional calculus for normal operators. This will be the only part of the book in which we will require some results of the theory of Banach algebras, or more specifically, C∗-algebras. These have been gathered in Appendix A.5.
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References
W. Arveson, A Short Course of Spectral Theory (Springer, New York, 2002)
K. Maurin, Methods of Hilbert Spaces (Polish Scientific Publishers, Warsaw, 1972)
G.K. Pedersen, Analysis Now (Springer, New York, 1995)
W. Rudin, Functional Analysis (McGraw-Hill, New York, 1991)
W. Żelazko, Banach Algebras (Polish Scientific Publishers, Warsaw, 1973)
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Sołtan, P. (2018). Functional Calculus for Families of Operators. In: A Primer on Hilbert Space Operators. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-92061-0_7
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DOI: https://doi.org/10.1007/978-3-319-92061-0_7
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