Abstract and Applied Analysis
Volume 2008 (2008), Article ID 651294, 11 pages
doi:10.1155/2008/651294
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
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 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)}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 l1 are finite-dimensional.