Counterexample to the spectral mapping theorem for the exponential function

Hejtmanek, J.; Kaper, Hans G.

doi:10.1090/S0002-9939-1986-0826482-1

Counterexample to the spectral mapping theorem for the exponential function
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by J. Hejtmanek and Hans G. Kaper PDF

Proc. Amer. Math. Soc. 96 (1986), 563-568 Request permission

Abstract:

An example is given of an unbounded operator in a Hilbert space which generates a strongly continuous semigroup and for which the spectral mapping theorem for the exponential function does not hold. The spectra of both the generator and the semigroup are determined explicitly.

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