Geodesic
Biorthogonal Systems in lp -Spaces
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 625-638

Voir la notice de l'article provenant de la source Cambridge University Press

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 ls with 1 < r <2 and 2 < s = r/(r – 1). 
Keown, R.; Conatser, C. Biorthogonal Systems in lp -Spaces. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 625-638. doi: 10.4153/CJM-1969-071-6
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