On some properties of quotients of homogeneous C(K) spaces

• Autorzy: Artur Michalak
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

nonseparable C(K) spaces; quotients of C(K) spaces

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B26: Nonseparable Banach spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2016
• Tom: 36
• Numer: 1
• Strony: 33-43

Daty

wydano

2016

otrzymano

2016-01-12

poprawiono

2016-04-31

Twórcy

autor

Artur Michalak

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

Bibliografia

• [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
• [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
• [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

Identyfikatory

DOI

10.7151/dmdico.1180