On positive embeddings of C(K) spaces

Grzegorz Plebanek

Studia Mathematica (2013)

  • Volume: 216, Issue: 2, page 179-192
  • ISSN: 0039-3223

Abstract

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We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such as countable tightness or Fréchetness, are inherited by K. We show that some isomorphic embeddings C(K) → C(L) can be, in a sense, reduced to positive embeddings.

How to cite

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Grzegorz Plebanek. "On positive embeddings of C(K) spaces." Studia Mathematica 216.2 (2013): 179-192. <http://eudml.org/doc/286133>.

@article{GrzegorzPlebanek2013,
abstract = { We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such as countable tightness or Fréchetness, are inherited by K. We show that some isomorphic embeddings C(K) → C(L) can be, in a sense, reduced to positive embeddings. },
author = {Grzegorz Plebanek},
journal = {Studia Mathematica},
keywords = {Banach space of continuous functions; positive operator; isomorphic embedding},
language = {eng},
number = {2},
pages = {179-192},
title = {On positive embeddings of C(K) spaces},
url = {http://eudml.org/doc/286133},
volume = {216},
year = {2013},
}

TY - JOUR
AU - Grzegorz Plebanek
TI - On positive embeddings of C(K) spaces
JO - Studia Mathematica
PY - 2013
VL - 216
IS - 2
SP - 179
EP - 192
AB - We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such as countable tightness or Fréchetness, are inherited by K. We show that some isomorphic embeddings C(K) → C(L) can be, in a sense, reduced to positive embeddings.
LA - eng
KW - Banach space of continuous functions; positive operator; isomorphic embedding
UR - http://eudml.org/doc/286133
ER -

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