Abstract
Normality says that ∥Af∥ = ∥A*f∥ for every vector f. It follows that ∥(A — λX)f∥ = ∥(A* — λ*)f∥ for every A, and hence that Π0(A) = (Π0(A*))*. The conclusion follows from Solution 73.
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© 1982 Springer-Verlag New York Inc.
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Halmos, P.R. (1982). Examples of Spectra. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9330-6_60
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DOI: https://doi.org/10.1007/978-1-4684-9330-6_60
Publisher Name: Springer, New York, NY
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