Displaying similar documents to “ M ( r , s ) -ideals of compact operators”

Unconditional ideals of finite rank operators

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

Czechoslovak Mathematical Journal

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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 .

M -ideals of compact operators into ℓ p

Kamil John, Dirk Werner (2000)

Czechoslovak Mathematical Journal

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We show for 2 ≤ p < ∞ and subspaces X of quotients of L p with a 1 -unconditional finite-dimensional Schauder decomposition that K ( X , ℓ p ) is an M -ideal in L ( X , ℓ p ) .

Strict u-ideals in Banach spaces

Vegard Lima, Åsvald Lima (2009)

Studia Mathematica

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We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition X * * * = X * ⊕ X ⊥ is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c₀. We also show that ℓ ∞ is not a u-ideal.

Unconditional ideals in Banach spaces

G. Godefroy, N. Kalton, P. Saphar (1993)

Studia Mathematica

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We show that a Banach space with separable dual can be renormed to satisfy hereditarily an “almost” optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition X * * * = X ⊥ ⊕ X * is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel X ⊥ . We undertake a general study of h-ideals and u-ideals. For example...