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On the Classification of Biorthogonal Sequences

Published online by Cambridge University Press:  20 November 2018

William H. Ruckle
William H. Ruckle*
Affiliation:
Clemson University, Clemson, South Carolina
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The work of various authors (e.g. Frink [3] and Markushevitch [7]) suggests the possibility of studying complete biorthogonal sequences in Banach spaces as a generalization of orthogonal families of continuous functions. But except for the case where the complete biorthogonal sequence is a Schauder basis such studies have not led to a very rich theory. The main reason for this is that an arbitrary complete biorthogonal sequence is not likely to have many helpful properties. For instance, in every separable Banach space X one can find a complete biorthogonal sequence {ei, Ei} which is not one-summable.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 721 - 733
Copyright
Copyright © Canadian Mathematical Society 1974

References

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