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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
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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| _version_ | 1849696392635744256 |
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| author | Diómedes Bárcenas Luis Gerardo Mármol |
| author_facet | Diómedes Bárcenas Luis Gerardo Mármol |
| author_sort | Diómedes Bárcenas |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-c81d273d50724fbb9dc7eb1e33b700bc |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c81d273d50724fbb9dc7eb1e33b700bc2025-08-20T03:19:29ZengWileyAbstract 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 |
| spellingShingle | Diómedes Bárcenas Luis Gerardo Mármol On the Adjoint of a Strongly Continuous Semigroup Abstract and Applied Analysis |
| title | 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_short | On the Adjoint of a Strongly Continuous Semigroup |
| title_sort | on the adjoint of a strongly continuous semigroup |
| url | http://dx.doi.org/10.1155/2008/651294 |
| work_keys_str_mv | AT diomedesbarcenas ontheadjointofastronglycontinuoussemigroup AT luisgerardomarmol ontheadjointofastronglycontinuoussemigroup |