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Basic sequences and subspaces in Lorentz sequence spaces without local convexity. (English) Zbl 0461.46006


MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
46A04 Locally convex Fréchet spaces and (DF)-spaces
46A35 Summability and bases in topological vector spaces
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
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[1] Zvi Altshuler, P. G. Casazza, and Bor Luh Lin, On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math. 15 (1973), 140 – 155. · Zbl 0264.46011
[2] G. Bennett, An extension of the Riesz-Thorin theorem, Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976) Springer, Berlin, 1977, pp. 1 – 11. Lecture Notes in Math., Vol. 604.
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[9] Bernard Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces \?^{\?}, Société Mathématique de France, Paris, 1974 (French). With an English summary; Astérisque, No. 11. · Zbl 0278.46028
[10] Stefan Rolewicz, Metric linear spaces, PWN-Polish Scientific Publishers, Warsaw, 1972. Monografie Matematyczne, Tom. 56. [Mathematical Monographs, Vol. 56]. · Zbl 0226.46001
[11] Helmut H. Schaefer, Banach lattices and positive operators, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 215. · Zbl 0296.47023
[12] W. J. Stiles, On properties of subspaces of \?_{\?},0<\?<1, Trans. Amer. Math. Soc. 149 (1970), 405 – 415. · Zbl 0205.12101
[13] Bertram Walsh, On characterizing Köthe sequence spaces as vector lattices, Math. Ann. 175 (1968), 253 – 256. · Zbl 0153.44001
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