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Symmetric Coordinate Spaces and Symmetric Bases

Published online by Cambridge University Press:  20 November 2018

William Ruckle
William Ruckle*
Affiliation:
Lehigh University, Bethlehem, Pennsylvania
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In this paper properties of symmetric coordinate spaces and symmetric bases are investigated. Since a space which possesses a basis is essentially a space of sequences (12, p. 207), the interrelation of these two concepts naturally suggests itself.

Section 2 is a summary of the terminology and methods employed, which fall into four categories: (1) set theoretical properties of coordinate spaces such as symmetry and dual spaces; (2) the notion of FK and BK space (12, p. 202; 13); (3) the theory of the Schauder basis in F-space applied to the case when (see § 2) is a basis for a coordinate space; (4) the concept of a sequential norm, which the author introduced in (7) to illustrate the underlying unity of the first three ideas.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 828 - 838
Copyright
Copyright © Canadian Mathematical Society 1967

References

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