On decompositions of Banach spaces into a sum of operator ranges

V. P. Fonf, V. V. Shevchik

Research output: Contribution to journalArticlepeer-review

Abstract

It is proved that a separable Banach space X admits a representation X = X1 + X2 as a sum (not necessarily direct) of two infinite-codimensional closed subspaces X1 and X2 if and only if it admits a representation X = A1(Y1) + A2(Y2) as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation X = T1(Z1) + T2(Z2) such that neither of the operator ranges T1(Z1), T2(Z2) contains an infinite-dimensional closed subspace if and only if X does not contain an isomorphic copy of l1.

Original languageEnglish
Pages (from-to)91-100
Number of pages10
JournalStudia Mathematica
Volume132
Issue number1
DOIs
StatePublished - 1 Jan 1999

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