Geodesic
Unconditional ideals of finite rank operators
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1257-1278 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $X$ be a Banach space. We give characterizations of when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal W}(Y,X)$ for every Banach space $Y$ in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when ${\cal F}(X,Y)$ is a $u$-ideal in ${\cal W}(X,Y)$ for every Banach space $Y$, when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal W}(Y,X^{**})$ for every Banach space $Y$, and when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal K}(Y,X^{**})$ for every Banach space $Y$.
Let $X$ be a Banach space. We give characterizations of when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal W}(Y,X)$ for every Banach space $Y$ in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when ${\cal F}(X,Y)$ is a $u$-ideal in ${\cal W}(X,Y)$ for every Banach space $Y$, when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal W}(Y,X^{**})$ for every Banach space $Y$, and when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal K}(Y,X^{**})$ for every Banach space $Y$.
Classification : 46B04, 46B20, 46B28, 47L20
Keywords: $u$-ideals; finite rank; compact; and weakly compact operators; Hahn-Banach extension operators 
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Abrahamsen, Trond A.; Lima, Asvald; Lima, Vegard. Unconditional ideals of finite rank operators. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1257-1278. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a29/

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