On some properties of quotients of homogeneous C(K) spaces
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)
- Volume: 36, Issue: 1, page 33-43
- ISSN: 1509-9407
Access Full Article
top
Abstract
topHow to cite
topArtur Michalak. "On some properties of quotients of homogeneous C(K) spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.1 (2016): 33-43. <http://eudml.org/doc/286955>.
@article{ArturMichalak2016,
abstract = {We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic to the space C([0,1]), then the quotient space X/Y contains a subspace isomorphic to the space C(K).},
author = {Artur Michalak},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {nonseparable C(K) spaces; quotients of C(K) spaces},
language = {eng},
number = {1},
pages = {33-43},
title = {On some properties of quotients of homogeneous C(K) spaces},
url = {http://eudml.org/doc/286955},
volume = {36},
year = {2016},
}
TY - JOUR
AU - Artur Michalak
TI - On some properties of quotients of homogeneous C(K) spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2016
VL - 36
IS - 1
SP - 33
EP - 43
AB - We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic to the space C([0,1]), then the quotient space X/Y contains a subspace isomorphic to the space C(K).
LA - eng
KW - nonseparable C(K) spaces; quotients of C(K) spaces
UR - http://eudml.org/doc/286955
ER -
References
top- [1] H.H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15. doi: 10.1090/S0002-9947-1961-0132375-5 Zbl0104.08502
- [2] R. Engelking, General Topology (Monografie Matematyczne 60, PWN - Polish Scientific Publishers, Warszawa, 1977).
- [3] L. Gillman and M. Jerison, Rings of Continuous Functions (D. Van Nostrand Company, INC. Princeton, N.J.-Toronto-New York-London, 1960).
- [4] J.L. Kelley, General Topology (D. Van Nostrand Company, Inc., Toronto-New YorkLondon, 1955).
- [5] J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Funct. Anal. 8 (1971), 225-249. doi: 10.1016/0022-1236(71)90011-5
- [6] A. Michalak, On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity, Studia Math. 155 (2003), 171-182. doi: 10.4064/sm155-2-6 Zbl1039.46012
- [7] A. Michalak, On uncomplemented isometric copies of c0 in spaces of continuous functions on products of the two-arrows space, Indagationes Math. 26 (2015), 162-173. doi: 10.1016/j.indag.2014.09.003 Zbl1326.46016
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.