The cofinal property of the reflexive indecomposable Banach spaces

Spiros A. Argyros[1]; Theocharis Raikoftsalis[1]

  • [1] National Technical University of Athens Faculty of Applied Sciences Department of Mathematics Zografou Campus, 157 80, Athens (Greece)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 1-45
  • ISSN: 0373-0956

Abstract

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It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably ℓ p -saturated space with 1 < p < ∞ and of a c 0 saturated space.

How to cite

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Argyros, Spiros A., and Raikoftsalis, Theocharis. "The cofinal property of the reflexive indecomposable Banach spaces." Annales de l’institut Fourier 62.1 (2012): 1-45. <http://eudml.org/doc/251064>.

@article{Argyros2012,
abstract = {It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell _p$-saturated space with $1&lt;p&lt;\infty $ and of a $c_0$ saturated space.},
affiliation = {National Technical University of Athens Faculty of Applied Sciences Department of Mathematics Zografou Campus, 157 80, Athens (Greece); National Technical University of Athens Faculty of Applied Sciences Department of Mathematics Zografou Campus, 157 80, Athens (Greece)},
author = {Argyros, Spiros A., Raikoftsalis, Theocharis},
journal = {Annales de l’institut Fourier},
keywords = {Banach space theory; $\ell _p$ saturated; indecomposable spaces; hereditarily indecomposable spaces; interpolation methods; saturated norms; saturated space; reflexive Banach space},
language = {eng},
number = {1},
pages = {1-45},
publisher = {Association des Annales de l’institut Fourier},
title = {The cofinal property of the reflexive indecomposable Banach spaces},
url = {http://eudml.org/doc/251064},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Argyros, Spiros A.
AU - Raikoftsalis, Theocharis
TI - The cofinal property of the reflexive indecomposable Banach spaces
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 1
EP - 45
AB - It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell _p$-saturated space with $1&lt;p&lt;\infty $ and of a $c_0$ saturated space.
LA - eng
KW - Banach space theory; $\ell _p$ saturated; indecomposable spaces; hereditarily indecomposable spaces; interpolation methods; saturated norms; saturated space; reflexive Banach space
UR - http://eudml.org/doc/251064
ER -

References

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