In the continuous case we prove that a strongly continuous uniformly
bounded semigroup of operators acting on a Hilbert space is
spectrally stable (i.e. the spectrum of its infinitesimal generator
lies in the open left half plane) if and only if for each
and each
one has:
Key Words: Spectral radius, discrete semigroups, strongly continuous semigroups, uniform exponential stability, Orlicz space.
2000 Mathematics Subject Classification: Primary: 47D03,
Secondary: 11M35.
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