Banach Spaces With Unique Unconditional Basis, Up to by J. Bourgain, P. G. Casazza, J. Lindenstrauss PDF

By J. Bourgain, P. G. Casazza, J. Lindenstrauss

ISBN-10: 082182323X

ISBN-13: 9780821823231

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Extra info for Banach Spaces With Unique Unconditional Basis, Up to Permutation

Example text

1'. 2. Let p > 1 and Ex < E2 < ' ' ' be finite subsets of the integers. For each n, let L^ be a linear operator from EnT^ into itself Then the operator L : 7 ^ -» 7 ^ , defined by oo x x € to - ZI Ln,En i ^ ^ ^ bounded if and only if sup ||Z

CASAZZA. UNDENSTRAUSS AND TZAFRIRI fl , . . , g{,m varies from 1 to 2 . To function identically equal to 1. e. 1, for all m and ;. ozi the empty set corresponds the the only function if the maximal if £ = 0). Clearly, the maximality of \ik\$~v we > c» where I * 3-(g+1>, for some 1 ^ m ^ 2*\. Since v is a probability measure and there are n - £ possible indices i it follows that there is a j 0 which belongs to at least e(n —£) distinct s e ts of the form A^. Since m takes 2^ values it follows that there is an m 0 and a set 6X c [l , .

CASAZZA, LINDENSTRAUSS AND TZAFKM rsj / \ f XiAs) ^ . j ^ ' "" 10 if ; & Ni and s ^ A . , otherwise We ihave t k a t ^S^H ^ 1, for all t, an

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Banach Spaces With Unique Unconditional Basis, Up to Permutation by J. Bourgain, P. G. Casazza, J. Lindenstrauss


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