ON SUBSPACES OF c0 AND EXTENSION OF OPERATORS INTO C(K )-SPACES
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چکیده
Johnson and Zippin recently showed that if X is a weak∗-closed subspace of 1 and T : X → C(K ) is any bounded operator then T can be extended to a bounded operator T̃ : 1 → C(K ). We give a converse result: if X is a subspace of 1 such that 1/X has an unconditional finitedimensional decomposition (UFDD) and every operator T : X → C(K ) can be extended to 1 then there is an automorphism τ of 1 such that τ(X) is weak ∗-closed. This result is proved by studying subspaces of c0 and several different characterizations of such subspaces are given.
منابع مشابه
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تاریخ انتشار 2001