(1+)-complemented, (1+)-isomorphic copies of L1 in dual Banach spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00562913" target="_blank" >RIV/67985840:_____/22:00562913 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00013-022-01778-2" target="_blank" >https://doi.org/10.1007/s00013-022-01778-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00013-022-01778-2" target="_blank" >10.1007/s00013-022-01778-2</a>
Alternative languages
Result language
angličtina
Original language name
(1+)-complemented, (1+)-isomorphic copies of L1 in dual Banach spaces
Original language description
The present paper contributes to the ongoing programme of quantification of isomorphic Banach space theory focusing on the Hagler-Stegall characterisation of dual spaces containing complemented copies of L-1. As a corollary, we obtain the following quantitative version of the Hagler-Stegall theorem asserting that for a Banach space X, the following statements are equivalent:nnX contains almost isometric contains almost isometric copies of (circle plus(infinity)(n=1) l(infinity)(n))(l1),nnfor all epsilon > 0, X * contains a (1 + epsilon)-complemented, (1 + epsilon)-isomorphic copy of L-1,nnfor all epsilon > 0, X * contains a (1 + epsilon)-complemented, (1 + epsilon)-isomorphic copy of C[0, 1]*. Moreover, if X is separable, one may add the following assertion:nnfor all epsilon > 0, there exists a (1 + epsilon)-quotient map T : X -> C(Delta) so that T*[C(Delta)*] is (1 + epsilon)-complemented in X*, where Delta is the Cantor set
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archiv der Mathematik
ISSN
0003-889X
e-ISSN
1420-8938
Volume of the periodical
119
Issue of the periodical within the volume
5
Country of publishing house
CH - SWITZERLAND
Number of pages
11
Pages from-to
495-505
UT code for WoS article
000844903300001
EID of the result in the Scopus database
2-s2.0-85137976247