Continuous extension of a densely parameterized semigroup

Eliahu Levy; Orr Moshe Shalit

doi:10.1007/s00233-008-9093-1

Continuous extension of a densely parameterized semigroup

Eliahu Levy, Orr Moshe Shalit

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let S be a dense sub-semigroup of R₊, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R₊. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over R ₊.

Original language	English
Pages (from-to)	276-284
Number of pages	9
Journal	Semigroup Forum
Volume	78
Issue number	2
DOIs	https://doi.org/10.1007/s00233-008-9093-1
State	Published - 1 Mar 2009
Externally published	Yes

Keywords

Contraction semigroup
Densely defined
Nonlinear semigroup extension

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-008-9093-1

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abstract = "Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over R +.",

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author = "Eliahu Levy and Shalit, {Orr Moshe}",

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AU - Shalit, Orr Moshe

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PY - 2009/3/1

Y1 - 2009/3/1

N2 - Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over R +.

AB - Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over R +.

KW - Contraction semigroup

KW - Densely defined

KW - Nonlinear semigroup extension

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ER -

Continuous extension of a densely parameterized semigroup

Abstract

Keywords

ASJC Scopus subject areas

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