| Autor: |
Alspach, D., Benyamini, Y. |
| Zdroj: |
Israel Journal of Mathematics; Nov1988, Vol. 64 Issue 2, p179-194, 16p |
| Abstrakt: |
We introduce a geometrical property of norm one complemented subspaces of C( K) spaces which is useful for computing lower bounds on the norms of projections onto subspaces of C( K) spaces. Loosely speaking, in the dual of such a space if x* is a w* limit of a net ( x ) and x*= x*+ x* with | x*|=| x*| + | x*|, then we measure how efficiently the x 's can be split into two nets converging to x* and x*, respectively. As applications of this idea we prove that if for every ε>0, X is a norm (1+ ε) complemented subspace of a C( K) space, then it is norm one complemented in some C( K) space, and we give a simpler proof that a slight modification of an l -predual constructed by Benyamini and Lindenstrauss is not complemented in any C( K) space. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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