Banach spaces with a unique nontrivial decomposition
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- by Spiros A. Argyros and Theocharis Raikoftsalis PDF
- Proc. Amer. Math. Soc. 136 (2008), 3611-3620 Request permission
Abstract:
Motivated by a problem of P. Koszmider we introduce the class of quasi-prime Banach spaces. This class lies between the classes of prime and primary Banach spaces. It is shown that for every $1<p<\infty$ there exists a strictly quasi-prime separable reflexive Banach space $\mathfrak {X}_p$ such that $\ell _p$ is a complemented subspace of $\mathfrak {X}_p$. A similar result also holds for the case of $\ell _1$ and $c_0$. More generally, for every separable decomposable prime Banach space $Y$ not containing $\ell _1$ there exists a strictly quasi-prime $\mathfrak {X}_Y$ containing $Y$ as a complemented subspace. We also investigate the operators acting on these spaces as well as the complemented subspaces of their finite powers.References
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Additional Information
- Spiros A. Argyros
- Affiliation: Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, National Technical University of Athens, 157 80, Athens, Greece
- MR Author ID: 26995
- Email: sargyros@math.ntua.gr
- Theocharis Raikoftsalis
- Affiliation: Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, National Technical University of Athens, 157 80, Athens, Greece
- Email: th-raik@hotmail.com
- Received by editor(s): July 12, 2007
- Received by editor(s) in revised form: September 11, 2007
- Published electronically: June 2, 2008
- Additional Notes: This work was partially supported by the Leukippos NTUA Research programme.
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3611-3620
- MSC (2000): Primary 46B20, 46B26
- DOI: https://doi.org/10.1090/S0002-9939-08-09368-4
- MathSciNet review: 2415045