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Biorthogonal Systems in lp-Spaces
- Source :
- Canadian Journal of Mathematics. 21:625-638
- Publication Year :
- 1969
- Publisher :
- Canadian Mathematical Society, 1969.
-
Abstract
- Our aim in this paper is to generalize certain ideas and results of Bary (1) on biorthogonal systems in separable Hilbert spaces to their counterparts in separable lp-spaces, 1 < p.The main result of Bary is to characterize a natural generalization of the concept of orthonormal basis for a Hilbert space. That of this paper is to characterize the concept of a Bary basis which is a generalization of the idea of standard basis of an lp-space. The result is interesting for lp-spaces because of the paucity of standard bases in these spaces.Before summarizing our results, we shall introduce some notation and recall a few pertinent definitions and facts. The symbols and denote mutually conjugate lp-spaces, where is the space lt and the space lswith 1 < r <2 and 2 < s = r/(r – 1).
- Subjects :
- Pure mathematics
Basis (linear algebra)
General Mathematics
010102 general mathematics
Hilbert space
Space (mathematics)
01 natural sciences
Separable space
symbols.namesake
Biorthogonal system
0103 physical sciences
Standard basis
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
symbols
Orthonormal basis
010307 mathematical physics
0101 mathematics
Lp space
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 21
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........5f7fa94c19f870e30ad6f378d4196e95