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Zbl 0675.47033
Kantorovitz, Shmuel
The Hille-Yosida space of an arbitrary operator. (English)
[J] J. Math. Anal. Appl. 136, No.1, 107-111 (1988). ISSN 0022-247X

Summary: Let A be an arbitrary Banach space operator with resolvent defined for all $\lambda >0$. We define a linear manifold Z in the given space and norm $\Vert\vert \cdot \Vert\vert$ on Z majorizing the given norm, such that (Z,$\Vert\vert \cdot \Vert\vert)$ is a Banach space, and the restriction of A to Z generates a strongly continuous semigroup of contractions in Z. This so-called Hille-Yosida space (Z,$\Vert\vert \cdot \Vert\vert)$ is ``maximal- unique'' in a suitable sense.

MSC 2000:: *47D03 (Semi)groups of linear operators

Keywords: strongly continuous semigroup of contractions; Hille-Yosida space; maximal-unique

Cited in: Zbl 0765.34041

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