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Logarithms and imaginary powers of operators on Hilbert spaces. (English) Zbl 0819.47018

Summary: We provide a necessary and sufficient condition for the existence of bounded imaginary powers of certain Hilbert space operators and study the growth of \(\| A^{it}\|\) when \(| t|\to\infty\).

MSC:

47A60 Functional calculus for linear operators
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