$M(r,s)$-ideals of compact operators

Rainis Haller; Marje Johanson; Eve Oja

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

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 $Y$ .

The space of compact operators as an M-ideal in its bidual.

T. S. S. R. K. Rao (1992)

Extracta Mathematicae

Similarity:

$M$ -ideals of compact operators into $ℓ_{p}$

Kamil John, Dirk Werner (2000)

Czechoslovak Mathematical Journal

Similarity:

We show for $2 \leq p < \infty$ 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

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 $X * * * = X * \oplus X^{⊥}$ 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 $ℓ_{\infty}$ is not a u-ideal.

Unconditional ideals in Banach spaces

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

Studia Mathematica

Similarity:

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 $X * * * = X^{⊥} \oplus X *$ 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...

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

Unconditional ideals of finite rank operators

The space of compact operators as an M-ideal in its bidual.

M -ideals of compact operators into ℓ p

Strict u-ideals in Banach spaces

Unconditional ideals in Banach spaces

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

$M$ -ideals of compact operators into $ℓ_{p}$