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Our aim is to prove that for any fixed 1/2 < α < 1 there exists a Hilbert space contraction T such that σ(T) = 1 and
.
This answers Zemánek’s question on the time regularity property.
In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator on a Hilbert space with a single spectrum satisfies
We prove that some regularity conditions on unbounded representations of topological abelian semigroups with countable spectral conditions induce a certain stability result extending the well-known Arendt-Batty-Lyubich-Vũ theorem.
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