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On the Construction of Sequence Spaces that have Schauder Bases

Published online by Cambridge University Press:  20 November 2018

William Ruckle
William Ruckle*
Affiliation:
Lehigh University, Bethlehem, Pa
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It is known that every Banach space which possesses a Schauder basis is essentially a space of sequences (6, Section 11.4). The primary objectives of this paper are: (1) to illustrate the close connection between sectionally bounded BK spaces and Banach spaces which have a Schauder basis, and (2) to consider some results in these theories in such a way as to render them easy and natural. In order to reach the largest number of readers we shall use (6) as the sole basis of our discussion. References to other authors are made in order to direct the reader to the original source of a theorem or to a related discussion.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1281 - 1293
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bessaga, C. and Pelczynski, A., A generalization of results of R. C. James concerning absolute bases in Banach spaces, Studia Math., 17 (1958), 165–174.Google Scholar
2. Day, Mahlon M., Normed linear spaces (New York, 1962).Google Scholar
3. James, R. C., Bases and reflexivity of Banach spaces, Ann. of Math. (2), 52 (1950), 518–527.Google Scholar
4. Sargent, W. L. C., On sectionally bounded BK spaces, Math. Z., 83 (1964), 57–66.Google Scholar
5. Singer, I., Some characterizations of symmetric bases in Banach spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys., 10 (1962), 185–192.Google Scholar
6. Wilansky, Albert, Functional analysis (New York, 1964).Google Scholar