Banach spaces in which a theorem of orlicz is not true |
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Authors: | S A Rakov |
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Institution: | 1. Khar'kov State University, USSR
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Abstract: | Let the Banach space X be such that for every numerical sequencet n ↘0 there exists in X an unconditionally convergent series σxn, the terms of which are subject to the condition ∥xn∥=tn (n=1,2,...). Then $$\mathop {sup}\limits_n \mathop {inf}\limits_{X_n } d(X_n ,l_\infty ^n )< \infty ,$$ where Xn ranges over all the n-dimensional subspaces of X. |
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