Abstract
In this chapter we will introduce by far the most important tool of the theory of operators on Hilbert space, namely functional calculus for self-adjoint operators. We begin with slightly more general considerations focused on normal operators which we will revisit later in Chapter 7.
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Notes
- 1.
Restriction of a compact operator to an invariant subspace clearly is compact.
References
W. Arveson, An Invitation to C∗-Algebras (Springer, New York, 1976)
W. Arveson, A Short Course of Spectral Theory (Springer, New York, 2002)
P. Halmos, A Hilbert Space Problem Book (Springer, New York, 1982)
G.K. Pedersen, Analysis Now (Springer, New York, 1995)
M. Reed, B. Simon, Methods of Modern Mathematical Physics I. Functional Analysis (Academic Press, London, 1980)
W. Rudin, Functional Analysis (McGraw-Hill, New York, 1991)
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Sołtan, P. (2018). Continuous Functional Calculus. In: A Primer on Hilbert Space Operators. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-92061-0_2
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DOI: https://doi.org/10.1007/978-3-319-92061-0_2
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