Semigroups of operators on locally convex spaces

Babalola, V. A.

doi:10.1090/S0002-9947-1974-0383142-8

Semigroups of operators on locally convex spaces
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by V. A. Babalola PDF

Trans. Amer. Math. Soc. 199 (1974), 163-179 Request permission

Abstract:

Let $X$ be a complex Hausdorff locally convex topological linear space and $L(X)$ the family of all continuous linear operators on $X$. This paper discusses the generation and perturbation theory for ${C_0}$ semigroups $\{ S(\xi ):\xi \geqslant 0\} \subset L(X)$ such that for each continuous seminorm $p$ on $X$ there exist a positive number ${\sigma _p}$ and a continuous seminorm $q$ on $X$ with $p(S(\xi )x) \leqslant {e^{^\sigma {p^\xi }}}q(x)$ for all $\xi \geqslant 0$ and $x \in X$. These semigroups are studied by means of a realization of $X$ as a projective limit of Banach spaces, using certain naturally-defined operators and ${C_0}$ semigroups on these Banach spaces to connect the present results to the classical Hille-Yosida-Phillips theory.

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Semigroups of operators in locally convex spaces

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