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Orlicz sequence spaces of Banach-Saks type. (English) Zbl 0735.46009
It is shown that in Orlicz sequence spaces of Banach-Saks type $p$, weakly null sequences admit of $p$- Hilbertian subsequences.
Reviewer: H.Knaust (El Paso)

MSC:
46B45Banach sequence spaces
WorldCat.org
Full Text: DOI
References:
[1] J.Elton, Weakly null normalized sequences in Banach spaces. Dissertation, Yale University 1978.
[2] B. V. Godun andS. A. Rakov, Banach-Saks property and the problem of three spaces. Mat. Zametki31, 61-74 (1982). English translation in: Math. Notes31, 32-39 (1982). · Zbl 0493.46015
[3] W. B. Johnson, On quotients ofL p which are quotients ofl p . Compositio Math.34, 69-89 (1977). · Zbl 0375.46023
[4] H.Knaust and E.Odell, Weakly null sequences with upperl p -estimates. In: E. Odell, H. Rosenthal (eds.), ?Functional Analysis, Proceedings, The University of Texas at Austin, 1987-89?, 85-107, Berlin-Heidelberg-New York 1991. · Zbl 0759.46013
[5] J.Lindenstrauss and L.Tzafriri, Classical Banach Spaces I. Berlin-Heidelberg-New York 1977. · Zbl 0362.46013
[6] E.Odell, Applications of Ramsey theorems to Banach space theory. In: H. E. Lacey (ed.), ?Notes in Banach Spaces?, 379-404, Austin-London 1981.
[7] S. A. Rakov, Banach-Saks property of a Banach space. Mat. Zametki26, 823-834 (1979). English translation in: Math. Notes26, 909-916 (1979). · Zbl 0421.46013
[8] S. A. Rakov, Banach-Saks exponent of certain Banach spaces of sequences. Mat. Zametki32, 613-625 (1982). English translation in: Math. Notes32, 791-797 (1982). · Zbl 0505.46005