Abstract and Applied Analysis
Volume 2008 (2008), Article ID 651294, 11 pages
Research Article

On the Adjoint of a Strongly Continuous Semigroup

Diómedes Bárcenas1 and Luis Gerardo Mármol2

1Universidad de los Andes, Mérida, Venezuela
2Universidad Simón Bolivar, Caracas, Venezuela

Received 1 December 2006; Revised 14 November 2007; Accepted 9 December 2007

Academic Editor: Simeon Reich

Copyright © 2008 Diómedes Bárcenas and Luis Gerardo Mármol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 l1; 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)}t0, 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 l1 are finite-dimensional.