Vol. 60, No. 2, 1975

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Unconditional Schauder decompositions of normed ideals of operators between some lp-spaces

Y. Gordon

Vol. 60 (1975), No. 2, 71–82
Abstract

Given a Banach space E, let

                    ∑N   ∘-----
l(E ) = sup  i{nPf} sup ∥   ±  r(Pi)Pi∥
F∈ℱ(E)  iN,±  i=1

where (E) denotes the collection of all finite-dimensional subspaces of E, the infimum ranges over all possible sequences of finite-rank operators Pi : F E which satisfy the equality Pi(f) = f for all f F, and r(P) denotes the rank of an operator P.

It is shown that there are finite-dimensional spaces with arbitrarily large l(E) values, and infinite-dimensional spaces E with l(E) = . The specific examples with l(E) = yield also information on the rapidity of growth of unconditional Schauder decompositions of E into finite-dimensional spaces.

Mathematical Subject Classification 2000
Primary: 47D15
Secondary: 46B15
Milestones
Received: 29 April 1975
Published: 1 October 1975
Authors
Y. Gordon