Abstract
We examine the symmetric basic sequences in some classes of Banach spaces with symmetric bases. We show that the Lorentz sequence spaced(a,p) has a unique symmetric basis and every infinite dimensional subspace ofd(a,p) contains a subspace isomorphic tol p. The symmetric basic sequences ind(a,p) are identified and a necessary and sufficient condition for a Lorents sequence space with exactly two nonequivalent symmetric basic sequences in given. We conclude by exhibiting an example of a Lorentz sequence space having a subspace with symmetric basis which is not isomorphic either to a Lorentz sequence space or to anl p-space.
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This is part of the first author's Ph. D. thesis, prepared at the Hebrew University of Jerusalem under the supervision of Dr. L. Tzafriri.
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Altshuler, Z., Casazza, P.G. & Lin, BL. On symmetric basic sequences in Lorentz sequence spaces. Israel J. Math. 15, 140–155 (1973). https://doi.org/10.1007/BF02764600
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DOI: https://doi.org/10.1007/BF02764600