Abstract of a paper by Jesus M.F. Castillo, and Yolanda Moreno
This is an announcement for the paper "On the bounded approximation property in Banach spaces" by Jesus M.F. Castillo, and Yolanda Moreno. Abstract: We prove that the kernel of a quotient operator from an $\mathcal L_1$-space onto a Banach space $X$ with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky --case $\ell_1$-- and Figiel, Johnson and Pe\l czy\'nski --case $X^*$ separable. Given a Banach space $X$, we show that if the kernel of a quotient map from some $\mathcal L_1$-space onto $X$ has the BAP then every kernel of every quotient map from any $\mathcal L_1$-space onto $X$ has the BAP. The dual result for $\mathcal L_\infty$-spaces also hold: if for some $\mathcal L_\infty$-space $E$ some quotient $E/X$ has the BAP then for every $\mathcal L_\infty$-space $E$ every quotient $E/X$ has the BAP. Archive classification: math.FA Remarks: To appear in Israel Journal of Mathematics Submitted from: castillo@unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4383 or http://arXiv.org/abs/1307.4383
participants (1)
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alspach@math.okstate.edu