Abstract
If A is an operator, then
Proof. If λ ∈ Π0(A*), then A*− λ has a non-zero kernel, and therefore the range of A − λ* has a non-zero orthogonal complement; both these implications are reversible.
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© 1982 Springer-Verlag New York Inc.
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Halmos, P.R. (1982). Properties 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_59
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DOI: https://doi.org/10.1007/978-1-4684-9330-6_59
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