Displaying similar documents to “Theorems of Hicks and LeChatelier-Samuelson type in ideal Banach spaces of infinite sequences.”

Unconditional ideals of finite rank operators

Trond A. Abrahamsen, Asvald Lima, Vegard Lima (2008)

Czechoslovak Mathematical Journal

Similarity:

Let X be a Banach space. We give characterizations of when ℱ ( Y , X ) is a u -ideal in 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 ℱ ( X , Y ) is a u -ideal in 𝒲 ( X , Y ) for every Banach space Y , when ℱ ( Y , X ) is a u -ideal in 𝒲 ( Y , X * * ) for every Banach space Y , and when ℱ ( Y , X ) is a u -ideal in 𝒦 ( Y , X * * ) for every Banach space Y .