Arcs defined by one-parameter semigroups of operators
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- by Hugo D. Junghenn and C. T. Taam PDF
- Proc. Amer. Math. Soc. 44 (1974), 113-120 Request permission
Abstract:
Let $T(t)(t \geqq 0)$ be a one-parameter semigroup of continuous linear operators in a locally convex reflexive linear topological space $X$ such that $T(c)$ is an isomorphism (into) for some $c > 0$. It is proved that for any $x \in X,T( \cdot )x$ is of bounded variation on finite intervals if and only if $x$ is in the domain of the infinitesimal generator of $T(t)$. The result is interpreted geometrically in terms of arc-length.References
- Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022
- Takako K\B{o}mura, Semigroups of operators in locally convex spaces, J. Functional Analysis 2 (1968), 258–296. MR 0234317, DOI 10.1016/0022-1236(68)90008-6
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 113-120
- MSC: Primary 47D05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0331114-7
- MathSciNet review: 0331114