Subsystems of the Walsh orthogonal system whose multiplicative completions are quasibases for ,

Authors:
M. G. Grigorian and Robert E. Zink

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1137-1149

MSC (2000):
Primary 42C10

DOI:
https://doi.org/10.1090/S0002-9939-02-06618-2

Published electronically:
July 25, 2002

MathSciNet review:
1948105

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Abstract | References | Similar Articles | Additional Information

Abstract: If one discards some of the elements from the Walsh family, an ancient example of a system that serves as a Schauder basis for each of the -spaces, with , the residual system will not be a Schauder basis for any of those spaces. Nevertheless, Price has shown that each member of a large class of such subsystems is complete on subsets of that have measure arbitrarily close to . In the present work, it is shown that subsystems of this kind can be multiplicatively completed in such a way that the resulting systems are quasibases for each space , , from which the earlier completeness result follows as a corollary.

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Additional Information

**M. G. Grigorian**

Affiliation:
Department of Mathematics, Erevan State University, Alex Manoogian Str., 375049 Yerevan, Armenia

Email:
gmarting@ysu.am

**Robert E. Zink**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1968

Email:
zink@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06618-2

Received by editor(s):
August 22, 2001

Received by editor(s) in revised form:
November 2, 2001

Published electronically:
July 25, 2002

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2002
American Mathematical Society