Abstract
If A is a diagonal operator, with Ae j = α j e j , then
So that {α j } is bounded and sup j |α j | ≦ ║A║. That reverse inequality follows from the relations
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© 1982 Springer-Verlag New York Inc.
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Halmos, P.R. (1982). Multiplication Operators. 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_57
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DOI: https://doi.org/10.1007/978-1-4684-9330-6_57
Publisher Name: Springer, New York, NY
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