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Classical Sequences in Banach Spaces (Chapman & Hall/CRC Pure and Applied Mathematics)
Classical Sequences in Banach Spaces (Chapman & Hall/CRC Pure and Applied Mathematics)
Date: 13 April 2011, 07:23

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Complete normed spaces, introduced by S. Banach in 1930, were expected to be very "regular": several structure theorems, true for all Banach spaces, were proved from 1930 to 1970, for example, by S. Banach himself, S. Banach and H. Steinhaus , A. Dvoretsky , A. Grothendieck. But in 1973, P. Enflo gave counterexamples to Banach's question: Does every Banach space have a basis? That showed that things were not as nice as expected. From then on, each time one thought to prove a structure theorem that would have showed more unity and more simplicity among Banach spaces, it happened to be false.

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