Abstract
A Banach spaceX with symmetric basis {e n} is isomorphic toc 0 orl p for some 1≦p<∞, if all symmetric basic sequences inX are equivalent to {e n}, and all symmetric basic sequences in [f n]≠X * are equivalent to {f n} (wheref n (e j ) =δ n, j ). The result proved in the paper is actually stronger, in the sense that it does not involve all symmetric basic sequences, but only the so called sequences generated by one vector.
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References
Z. Altshuler, P. G. Casazza and Bor Luh Lin,On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math.15 (1973), 140–155.
P. G. Casazza and Bor Luh Lin,On symmetric basic sequences in Lorentz sequence spaces II, Israel J. Math.17 (1974), 191–217.
J. Lindenstrauss and L. Tzafriri,On the complemented subspaces problem, Israel J. Math.9 (1971), 263–269.
J. Lindenstrauss and L. Tzafriri,Classical Banach spaces, Springer-Verlag Lecture Notes, No. 338, 1973.
M. Zippin,On perfectly homogeneous bases in Banach spaces, Israel J. Math.4 (1966), 265–275.
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This is part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor L. Tzafriri. I wish to thank Professor Tzafriri for his interest and advice.
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Altshuler, Z. Characterization ofc 0 andl p among Banach spaces with symmetric basis. Israel J. Math. 24, 39–44 (1976). https://doi.org/10.1007/BF02761427
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DOI: https://doi.org/10.1007/BF02761427