Abstract
Let $X$ be a complex Banach spcce, and denote by $T$ a strongly continuous semigroup of linear operators defined on $X$ and by $C$ a cosine function of operators with associated sine function $S$ defined on $X$. In this note we characterize in terms of spectral properties of the infinitesimal generator those semigroups $T$ and cosine functions $C$ such that $\{T(t) - I : t \geq 0 \}$, $\{C(t) - I : t \in {\Bbb R}\}\;$ and $\{S(t) : t \in {\Bbb R}\}$ are collectively compact sets of bounded linear operators.
Citation
Hernan R. Henriquez. "ON THE COLLECTIVE COMPACTNESS OF STRONGLY CONTINUOUS SEMIGROUPS AND COSINE FUNCTIONS OF OPERATORS." Taiwanese J. Math. 2 (4) 497 - 509, 1998. https://doi.org/10.11650/twjm/1500407020
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