Abstract
For the symmetric Xp,wn subspaces of L p , p > 2, we determine the dimension of their approximately Euclidean subspaces and estimate the smallest dimensions of their containing spaces. We also show that a diagonal of the canonical basis of , p > 2, with an unconditional basic sequence in L p whose span is complemented, spans a space which is isomorphic to a complemented subspace of L p .
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© 2004 Springer-Verlag Berlin/Heidelberg
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Johnson, W.B., Schechtman, G. (2004). Several Remarks Concerning the Local Theory of L p Spaces. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44489-3_13
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DOI: https://doi.org/10.1007/978-3-540-44489-3_13
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22360-3
Online ISBN: 978-3-540-44489-3
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