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On the Basis Problem for Vector Valued Function Spaces

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis
H. W. Ellis*
Affiliation:
Queen's University
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1. Introduction. In a recent paper (2) Halperin and the author considered separable Banach spaces Lλ of real valued functions on general measure spaces and proved the existence of 1-regular (§2) Haar or σ-Haar bases when λ was the classical p-norm or any levelling length function (3) and, more generally, of K-regular Haar or σ-Haar bases when λ was a continuous length function satisfying certain additional conditions (2, Theorem 3.2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 417 - 422
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Banach, Stefan, Théorie des opérations linéaires (Warsaw, 1932).Google Scholar
2. Ellis, H. W. and Halperin, Israel, Haar functions and the basis problem for Banach spaces, J. London Math. Soc, 31 (1956), 28–39.Google Scholar
3. Ellis, H. W. and Halperin, Israel, Function spaces determined by levelling length functions. Can. J. Math., 5 (1953), 576–592.Google Scholar
4. Hille, Einar, Functional analysis and semi-groups, Amer. Math. Soc. Coll. Publications, Vol. XXXI (New York, 1948).Google Scholar