Asymptotic Unconditionality
We show that a separable real Banach space embeds almost isometrically in a space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to \infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^* \in X^*$, $(x_n^*)$ is a weak$^*$-null sequence and both limits exist....
Saved in:
| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
12.09.2008
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We show that a separable real Banach space embeds almost isometrically in a
space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to
\infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^*
\in X^*$, $(x_n^*)$ is a weak$^*$-null sequence and both limits exist. If $X$
is reflexive then $Y$ can be assumed reflexive. These results provide the
isometric counterparts of recent work of Johnson and Zheng. |
|---|---|
| AbstractList | We show that a separable real Banach space embeds almost isometrically in a
space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to
\infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^*
\in X^*$, $(x_n^*)$ is a weak$^*$-null sequence and both limits exist. If $X$
is reflexive then $Y$ can be assumed reflexive. These results provide the
isometric counterparts of recent work of Johnson and Zheng. |
| Author | Cowell, S. R Kalton, N. J |
| Author_xml | – sequence: 1 givenname: S. R surname: Cowell fullname: Cowell, S. R – sequence: 2 givenname: N. J surname: Kalton fullname: Kalton, N. J |
| BackLink | https://doi.org/10.48550/arXiv.0809.2294$$DView paper in arXiv |
| BookMark | eNotzr0KgzAUhuEM7dDa7oVC6Q1oY4yajCL9A6GLneWYEyGgUVRKvfv-Th_v8vEsycy2VhOy8anHRRjSA_RP8_CooNJjTPIF2SbD1HRjOxq1v1vVWjSjaS3UZpxWZF5BPej1fx2Sn455enGz2_maJpkLUchdDISmkc9iKhWvaFCVUPpcYYgMESuGEKPgTApU-l0xjyiUCKiVz6UqdeCQ3e_2iyu63jTQT8UHWXyQwQv1rjmf |
| ContentType | Journal Article |
| Copyright | http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| Copyright_xml | – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.0809.2294 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 0809_2294 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-LOGICAL-a654-d38e0612709c4f03fbab14cd5d2dddf2da7d84298dcef2d7460abdadec149cbe3 |
| IEDL.DBID | GOX |
| IngestDate | Mon Jan 08 05:38:18 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a654-d38e0612709c4f03fbab14cd5d2dddf2da7d84298dcef2d7460abdadec149cbe3 |
| OpenAccessLink | https://arxiv.org/abs/0809.2294 |
| ParticipantIDs | arxiv_primary_0809_2294 |
| PublicationCentury | 2000 |
| PublicationDate | 2008-09-12 |
| PublicationDateYYYYMMDD | 2008-09-12 |
| PublicationDate_xml | – month: 09 year: 2008 text: 2008-09-12 day: 12 |
| PublicationDecade | 2000 |
| PublicationYear | 2008 |
| Score | 1.4350644 |
| SecondaryResourceType | preprint |
| Snippet | We show that a separable real Banach space embeds almost isometrically in a
space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Functional Analysis |
| Title | Asymptotic Unconditionality |
| URI | https://arxiv.org/abs/0809.2294 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV07T8MwED61nVgQFe_yyMBqSBzn4bGqKBUSsLRStuics6UOlKoNFfx7zkmKWBh9Plk6W_J939n-DHCnpaTIGCe8WhsTFNRCa2sEkoqy0CHmztc7Xl7T2UI9F0nRg9v9WxjcfC13rT6w2T4wnNH3UmrVh76U_sbW01vRHjY2Slyd-68bI8zG8idFTI_gsMN2wbhdjCH07OoYRuPt9_u6_mBbsFgx-6RlW35j-HsC8-njfDIT3Y8EAtNECYpz6yFBFupKuTB2Bk2kKkpIEpGThBnlvMHnVFluZSoN0RCSrZiHVMbGpzBgUm_PIUh1bInRjNOxU84hJwkeAE3uCzEyMhdw1kRSrlvRidLHWPoYL__tGcHB_jZDJK9gUG8-7TWnzNrcNBP3A-7WbVc |
| link.rule.ids | 228,230,783,888 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Asymptotic+Unconditionality&rft.au=Cowell%2C+S.+R&rft.au=Kalton%2C+N.+J&rft.date=2008-09-12&rft_id=info:doi/10.48550%2Farxiv.0809.2294&rft.externalDocID=0809_2294 |