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Unconditional basic sequence in $L^p({\mu})$
and its $l^p$-stability


Author: Lihua Yang
Journal: Proc. Amer. Math. Soc. 127 (1999), 455-464
MSC (1991): Primary 46B20
MathSciNet review: 1473673
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Abstract: This paper is concerned with unconditional basic sequences in $L^p(\mu )$. We prove that, under some conditions, a sequence in $L^p(\mu )$ is a bounded unconditional basic sequence if and only if it is $l^p$-stable. At last the results are applied to the shift-invariant basic sequences generated by a finite subset of $L^p(R^s)$, which is very important in wavelet analysis.


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Additional Information

Lihua Yang
Affiliation: Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, People’s Republic of China; Institute of Mathematics, Academy Sinica, Beijing, 100080, People’s Republic of China
Email: yang@comp.hkbu.edu.hk, ylh@math03.math.ac.cn

DOI: https://doi.org/10.1090/S0002-9939-99-04638-9
Keywords: Unconditional basic sequence, $l^p$-stability, wavelet analysis
Received by editor(s): October 14, 1996
Received by editor(s) in revised form: May 21, 1997
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1999 American Mathematical Society