| Title:
|
Adjoint bi-continuous semigroups and semigroups on the space of measures (English) |
| Author:
|
Farkas, Bálint |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
309-322 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a given bi-continuous semigroup $(T(t))_{t\geq 0}$ on a Banach space $X$ we define its adjoint on an appropriate closed subspace $X^\circ $ of the norm dual $X'$. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology $\sigma (X^\circ ,X)$. We give the following application: For $\Omega $ a Polish space we consider operator semigroups on the space ${\rm C_b}(\Omega )$ of bounded, continuous functions (endowed with the compact-open topology) and on the space ${\rm M}(\Omega )$ of bounded Baire measures (endowed with the weak$^*$-topology). We show that bi-continuous semigroups on ${\rm M}(\Omega )$ are precisely those that are adjoints of bi-continuous semigroups on ${\rm C_b}(\Omega )$. We also prove that the class of bi-continuous semigroups on ${\rm C_b}(\Omega )$ with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if $\Omega $ is not a Polish space this is not the case. (English) |
| Keyword:
|
not strongly continuous semigroups |
| Keyword:
|
bi-continuous semigroups |
| Keyword:
|
adjoint semigroup |
| Keyword:
|
mixed-topology |
| Keyword:
|
strict topology |
| Keyword:
|
one-parameter semigroups on the space of measures |
| MSC:
|
46A03 |
| MSC:
|
47D03 |
| MSC:
|
47D06 |
| MSC:
|
47D99 |
| idZBL:
|
Zbl 1249.47021 |
| idMR:
|
MR2905405 |
| DOI:
|
10.1007/s10587-011-0076-0 |
| . |
| Date available:
|
2011-06-06T10:25:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141535 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
