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2008 On the Adjoint of a Strongly Continuous Semigroup
Diómedes Bárcenas, Luis Gerardo Mármol
Abstr. Appl. Anal. 2008: 1-11 (2008). DOI: 10.1155/2008/651294

Abstract

Using some techniques from vector integration, we prove the weak measurability of the adjoint of strongly continuous semigroups which factor through Banach spaces without isomorphic copy of l 1 ; we also prove the strong continuity away from zero of the adjoint if the semigroup factors through Grothendieck spaces. These results are used, in particular, to characterize the space of strong continuity of { T * * ( t ) } t 0 , which, in addition, is also characterized for abstract L - and M -spaces. As a corollary, it is proven that abstract L -spaces with no copy of l 1 are finite-dimensional.

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Diómedes Bárcenas. Luis Gerardo Mármol. "On the Adjoint of a Strongly Continuous Semigroup." Abstr. Appl. Anal. 2008 1 - 11, 2008. https://doi.org/10.1155/2008/651294

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1165.47026
MathSciNet: MR2393113
Digital Object Identifier: 10.1155/2008/651294

Rights: Copyright © 2008 Hindawi

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