Spectral mapping theorems for exponentially bounded c-semigroups in Banach spaces |
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| Authors: | Ki Sik Ha |
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| Institution: | (1) Pusan National University, Pusan, Korea |
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| Abstract: | LetZ be a generator of an exponentially boundedC-semigroup {S
t
}
t≥0 in a Banach space and letT
t
=C
−1
S
t
. We show that the spectral mapping theorems such as exp(tσ(Z)) ⊂ σ(T
t
) and exp(tσ
p
(Z)) ⊂ tσ
p
(T
t
) ⊂ exp(tσ
p
(Z)) ⋃ {0} for everyt≥0 hold.
The present studies were supported by the Basic Science Research Institute Program, Ministry of Education, 1987. |
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| Keywords: | |
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