Extremal properties of the set of vector-valued Banach limits
In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the spac...
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2015-11-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2015-0067 |
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doaj-ca18d359a34a4e3bb67130330eb0458d2021-09-06T19:20:07ZengDe GruyterOpen Mathematics2391-54552015-11-0113110.1515/math-2015-0067math-2015-0067Extremal properties of the set of vector-valued Banach limitsGarcía-Pacheco Francisco Javier0Department of Mathematics, University of Cadiz, Puerto Real 11510, SpainIn this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set of vector-valued Banach limits is conducted when the underlying normed space is a Hilbert space.We also reach the conclusion that the set of vector-valued Banach limits is not a convex component of BCL(ℓ∞(X),X), provided that X is a 1-injective Banach space satisfying that the underlying compact Hausdorff topological space has isolated points.https://doi.org/10.1515/math-2015-0067banach limit almost convergence group of isometries extremal structure |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
García-Pacheco Francisco Javier |
| spellingShingle |
García-Pacheco Francisco Javier Extremal properties of the set of vector-valued Banach limits Open Mathematics banach limit almost convergence group of isometries extremal structure |
| author_facet |
García-Pacheco Francisco Javier |
| author_sort |
García-Pacheco Francisco Javier |
| title |
Extremal properties of the set
of vector-valued Banach limits |
| title_short |
Extremal properties of the set
of vector-valued Banach limits |
| title_full |
Extremal properties of the set
of vector-valued Banach limits |
| title_fullStr |
Extremal properties of the set
of vector-valued Banach limits |
| title_full_unstemmed |
Extremal properties of the set
of vector-valued Banach limits |
| title_sort |
extremal properties of the set
of vector-valued banach limits |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2015-11-01 |
| description |
In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits
different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first
need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which
turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set
of vector-valued Banach limits is conducted when the underlying normed space is a Hilbert space.We also reach the
conclusion that the set of vector-valued Banach limits is not a convex component of BCL(ℓ∞(X),X), provided that X
is a 1-injective Banach space satisfying that the underlying compact Hausdorff topological space has isolated points. |
| topic |
banach limit almost convergence group of isometries extremal structure |
| url |
https://doi.org/10.1515/math-2015-0067 |
| work_keys_str_mv |
AT garciapachecofranciscojavier extremalpropertiesofthesetofvectorvaluedbanachlimits |
| _version_ |
1717777327076671488 |