On the Adjoint of a Strongly Continuous Semigroup
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 Grothen...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/651294 |
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doaj-c81d273d50724fbb9dc7eb1e33b700bc2020-11-24T22:30:01ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/651294651294On the Adjoint of a Strongly Continuous SemigroupDiómedes Bárcenas0Luis Gerardo Mármol1Universidad de los Andes, Mérida, VenezuelaUniversidad Simón Bolivar, Caracas, VenezuelaUsing 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.http://dx.doi.org/10.1155/2008/651294 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Diómedes Bárcenas Luis Gerardo Mármol |
| spellingShingle |
Diómedes Bárcenas Luis Gerardo Mármol On the Adjoint of a Strongly Continuous Semigroup Abstract and Applied Analysis |
| author_facet |
Diómedes Bárcenas Luis Gerardo Mármol |
| author_sort |
Diómedes Bárcenas |
| title |
On the Adjoint of a Strongly Continuous Semigroup |
| title_short |
On the Adjoint of a Strongly Continuous Semigroup |
| title_full |
On the Adjoint of a Strongly Continuous Semigroup |
| title_fullStr |
On the Adjoint of a Strongly Continuous Semigroup |
| title_full_unstemmed |
On the Adjoint of a Strongly Continuous Semigroup |
| title_sort |
on the adjoint of a strongly continuous semigroup |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2008-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2008/651294 |
| work_keys_str_mv |
AT diomedesbarcenas ontheadjointofastronglycontinuoussemigroup AT luisgerardomarmol ontheadjointofastronglycontinuoussemigroup |
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1725742239254052864 |