Displaying similar documents to “ M -ideals of compact operators into ℓ p ”

Strict u-ideals in Banach spaces

Vegard Lima, Åsvald Lima (2009)

Studia Mathematica

Similarity:

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.

On an inclusion between operator ideals

Manuel A. Fugarolas (2011)

Czechoslovak Mathematical Journal

Similarity:

Let 1 ≤ q < p < ∞ and 1 / r : = 1 / p max ( q / 2 , 1 ) . We prove that ℒ r , p ( c ) , the ideal of operators of Geľfand type l r , p , is contained in the ideal Π p , q of ( p , q ) -absolutely summing operators. For q > 2 this generalizes a result of G. Bennett given for operators on a Hilbert space.

Projections from L ( X , Y ) onto K ( X , Y )

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let X and Y be Banach spaces such that X is weakly compactly generated Asplund space and X * has the approximation property (respectively Y is weakly compactly generated Asplund space and Y * has the approximation property). Suppose that L ( X , Y ) ≠ K ( X , Y ) and let 1 < λ < 2 . Then X (respectively Y ) can be equivalently renormed so that any projection P of L ( X , Y ) onto K ( X , Y ) has the sup-norm greater or equal to λ . ...

On the compact approximation property

Vegard Lima, Åsvald Lima, Olav Nygaard (2004)

Studia Mathematica

Similarity:

We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net ( S γ ) of compact operators on X such that s u p γ | | S γ T | | ≤ | | T | | and S γ → I X in the strong operator topology. Similar results for dual spaces are also proved.

An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property

J. Cabello, E. Nieto (1998)

Studia Mathematica

Similarity:

C.-M. Cho and W. B. Johnson showed that if a subspace E of ℓ p , 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with r 2 + s 2 < 1 , the James space can be provided with an equivalent norm such that an arbitrary subspace E has the metric compact approximation property iff there is a norm one projection P on ℒ(E)* with Ker P = K(E)⊥ satisfying ∥⨍∥ ≥ r∥Pf∥ + s∥φ - Pf∥ ∀⨍ ∈ ℒ(E)*. A similar result is proved for subspaces of...

Johnson's projection, Kalton's property (M*), and M-ideals of compact operators

Olav Nygaard, Märt Põldvere (2009)

Studia Mathematica

Similarity:

Let X and Y be Banach spaces. We give a “non-separable” proof of the Kalton-Werner-Lima-Oja theorem that the subspace (X,X) of compact operators forms an M-ideal in the space (X,X) of all continuous linear operators from X to X if and only if X has Kalton’s property (M*) and the metric compact approximation property. Our proof is a quick consequence of two main results. First, we describe how Johnson’s projection P on (X,Y)* applies to f ∈ (X,Y)* when f is represented via a Borel (with...