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Uniform and Equicontinuous Schauder Bases of Subspaces

Published online by Cambridge University Press:  20 November 2018

Charles W. McArthur  and
James R. Retherford
Charles W. McArthur
Affiliation:
Florida State University
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A sequence {Mi} of non-trivial subspaces of a linear topological space X is a basis of subspaces for X if and only if corresponding to each x ∊ X there is a unique sequence {xi}, xi ∊ Mi, such that

Corresponding to a basis of subspaces {Mi} for X is a sequence of orthogonal projections {Ei} (Ei2 = Ei and EiEj = 0 if i ≠ j) defined by Ei(x) = xi if

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 207 - 212
Copyright
Copyright © Canadian Mathematical Society 1965

References

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