n this paper, we characterize the condition (E) limμ→±∞∥R(iμ,A)∥=0 for a generator A of an exponentially stable semigroup (T(t))t≥0 on an arbitrary Banach space in terms of (T(t))t≥0. As shown earlier on Hilbert spaces this condition is equivalent to the norm continuity of the semigroup for t>0.
Towards a characterization of eventually norm continuous semigroups on Banach spaces
ENGEL, KLAUS JOCHEN OTTO;
1996-01-01
Abstract
n this paper, we characterize the condition (E) limμ→±∞∥R(iμ,A)∥=0 for a generator A of an exponentially stable semigroup (T(t))t≥0 on an arbitrary Banach space in terms of (T(t))t≥0. As shown earlier on Hilbert spaces this condition is equivalent to the norm continuity of the semigroup for t>0.File in questo prodotto:
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