Summary
In this paper we study the complemented subspaces of the spaces (lp)N∩lq(lq), with 1≤p<q≤∞ or q=0, thereby showing that if (lp)N∩lq(lq)=F⊕G then either F or G contains a complemented copy of the whole space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. A. Albanese,Primary products of Banach spaces, Arch. Math.,66 (1996), pp. 397–405.
D. Alspach—P. Enflo—E. Odell, On the structure of separable Lp spaces (1<p<∞), Studia Math.,60 (1977), pp. 79–90.
J. Bonet—S. Dierolf,Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid,2 (suppl.) (1989), pp. 77–92.
P. G. Casazza—Bor-Luh Lin,Projections on Banach spaces with symmetric bases, Studia Math.,52 (1974), pp. 189–193.
J. C. Díaz,On the three-space property: non-containment of l p, 1≤p<∞ orc 0 subspaces, Publ. Math.,37 (1993), pp. 127–132.
J. C. Díaz,Primariness of some universal Fréchet spaces, pp. 95–103 in Functional Analysis (Eds.: Dierolf/Dineen/Domański), Walter de Gruyter & Co., Berlin-New York, 1996.
P. Domanski—A. Ortynski,Complemented subspaces of products of Banach spaces, Trans. Amer. Math. Soc.,316 (1989), pp. 215–231.
I. S. Edelstein—P. Wojtaszczyk,On projections and unconditional bases in direct sums of Banach spaces, Studia Math.,56 (1976), pp. 263–276.
J. Lindenstrauss—L. Tzafriri,Classical Banach spaces I, Springer-Verlag, Berlin, Heidelberg, New York, (1977).
G. Metafune—V. B. Moscatelli,Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. (4),153 (1988), pp. 175–190.
G. Metafune—V. B. Moscatelli, On the space\(l^{p + } = \mathop \cap \limits_{q > p} l^q \), Math. Nachr.,147 (1990), pp. 47–50.
V. B. Moscatelli,Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc.,12 (1980), pp. 63–66.
Author information
Authors and Affiliations
Additional information
Entrata in Redazione il 19 aprile 1999. Ricevuta versione finale il 4 febbraio 2000.
Research supported by the Italian MURST.
Rights and permissions
About this article
Cite this article
Albanese, A.A., Moscatelli, V.B. On complemented subspaces of the spaces (l p)N∩l q(l q). Annali di Matematica pura ed applicata 179, 401–412 (2001). https://doi.org/10.1007/BF02505965
Issue Date:
DOI: https://doi.org/10.1007/BF02505965