Concerning biorthogonal systems in C(S)

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Biorthogonal Systems

Biorthogonal Systems in lp-Spaces

1969 ◽  
Vol 21 ◽  
pp. 625-638 ◽  
Author(s):  
R. Keown ◽  
C. Conatser
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Orthonormal Basis ◽  
Natural Generalization ◽  
Standard Basis ◽  
Biorthogonal Systems ◽  
Lp Spaces ◽  
Standard Bases

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).

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