Quotients of indecomposable Banach spaces of continuous functions

Rogério Augusto dos Santos Fajardo

Studia Mathematica (2012)

  • Volume: 212, Issue: 3, page 259-283
  • ISSN: 0039-3223

Abstract

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Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where C(K) has few operators and K contains a homeomorphic copy of βℕ.

How to cite

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Rogério Augusto dos Santos Fajardo. "Quotients of indecomposable Banach spaces of continuous functions." Studia Mathematica 212.3 (2012): 259-283. <http://eudml.org/doc/285382>.

@article{RogérioAugustodosSantosFajardo2012,
abstract = { Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where C(K) has few operators and K contains a homeomorphic copy of βℕ. },
author = {Rogério Augusto dos Santos Fajardo},
journal = {Studia Mathematica},
keywords = {Banach spaces of continuous functions; indecomposable Banach spaces; connectedness; diamond axiom; continuum hypothesis},
language = {eng},
number = {3},
pages = {259-283},
title = {Quotients of indecomposable Banach spaces of continuous functions},
url = {http://eudml.org/doc/285382},
volume = {212},
year = {2012},
}

TY - JOUR
AU - Rogério Augusto dos Santos Fajardo
TI - Quotients of indecomposable Banach spaces of continuous functions
JO - Studia Mathematica
PY - 2012
VL - 212
IS - 3
SP - 259
EP - 283
AB - Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where C(K) has few operators and K contains a homeomorphic copy of βℕ.
LA - eng
KW - Banach spaces of continuous functions; indecomposable Banach spaces; connectedness; diamond axiom; continuum hypothesis
UR - http://eudml.org/doc/285382
ER -

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