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- W4299623877 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 Pel 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." @default.
- W4299623877 created "2022-10-02" @default.
- W4299623877 creator A5030370971 @default.
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- W4299623877 date "2013-07-16" @default.
- W4299623877 modified "2023-10-16" @default.
- W4299623877 title "On the Bounded Approximation Property in Banach spaces" @default.
- W4299623877 doi "https://doi.org/10.48550/arxiv.1307.4383" @default.
- W4299623877 hasPublicationYear "2013" @default.
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