Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T02:36:32.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Schauder decompositions in non-separable Banach spaces

Published online by Cambridge University Press:  17 April 2009

J.J.M. Chadwick  and
R.W. Cross
J.J.M. Chadwick
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that Schauder decompositions exist in non-separable weakly compactly generated spaces and in certain non-separable conjugate spaces. Some results are obtained concerning shrinking and boundedly complete Schauder decompositions in non-separable spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 133 - 144
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Amir, D. and Lindenstrauss, J., “The structure of weakly compact sets in Banach spaces”, Ann. of Math. (2) 88 (1968), 35–46.CrossRefGoogle Scholar
[2]Bishop, Errett and Phelps, R.R., “A proof that every Banach space is subreflexive”, Bull. Amer. Math. Soc. 67 (1961), 97–98.Google Scholar
[3]Cudia, Dennis F., “The geometry of Banach spaces. Smoothness”, Trans. Amer. Math. Soc. 110 (1964), 284–314.Google Scholar
[4]Day, M.M., Narmed linear spaces (Springer-Verlag, Berlin, Göttingen, Heidelberg, 1958).CrossRefGoogle Scholar
[5]Dunford, Nelson and Schwartz, Jacob T., Linear operators, Part I (Interscience [John Wiley & Sons], New York, London, 1958).Google Scholar
[6]Rosenthal, Haskell P., “On injective Banach spaces and the spaces L∞ (μ) for finite measures μ”, Aata Math. 124 (1970), 205–248.Google Scholar
[7]Ruckle, William H., “The infinite sum of closed subspaces of an F-space”, Duke Math. J. 31 (1964), 543–554.CrossRefGoogle Scholar
[8]Sanders, B.L., “Decompositions and reflexivity in Banach spaces”, Proc. Amer. Math. Soc. 16 (1965), 204–208.CrossRefGoogle Scholar
[9]Tacon, D.G., “The conjugate of a smooth Banach space”, Bull. Austral. Math. Soc. 2 (1970), 415–425.CrossRefGoogle Scholar