The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces

DOI10.1016/j.jfa.2004.02.009zbMath1067.46026OpenAlexW2056502451MaRDI QIDQ1883422

Richard J. Loy, Niels Jakob Laustsen, Charles John Read

Publication date: 12 October 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://eprints.lancs.ac.uk/id/eprint/21081/1/closedideals.pdf

zbMATH Keywords

Banach algebraBanach spaceoperatorideal lattice

Mathematics Subject Classification ID

Spaces of operators; tensor products; approximation properties (46B28) Operator ideals (47L20) Algebras of operators on Banach spaces and other topological linear spaces (47L10) Ideals and subalgebras (46H10)

Related Items (17)

Classifying the closed ideals of bounded operators on two families of non-separable classical Banach spaces ⋮ A new complemented subspace for the Lorentz sequence spaces, with an application to its lattice of closed ideals ⋮ Closed ideals of operators on the Tsirelson and Schreier spaces ⋮ Uniqueness of the maximal ideal of operators on the ℓ_p-sum of ℓ_∞ⁿ (n ∈ ) for 1 < p < ∞ ⋮ Uniqueness of the maximal ideal of the Banach algebra of bounded operators on \(C([0, \omega_1)\)] ⋮ Maximal Ideals in Some Spaces of Bounded Linear Operators ⋮ Norm closed operator ideals in Lorentz sequence spaces ⋮ When are full representations of algebras of operators on Banach spaces automatically faithful? ⋮ Small operator ideals on the Schlumprecht and Schreier spaces ⋮ Norm closed ideals in the algebra of bounded linear operators on Orlicz sequence spaces ⋮ \(\pi\)-complemented algebras through pseudocomplemented lattices ⋮ Structure of modules over the stereotype algebra \({\mathcal L}(X)\) of operators ⋮ Closed ideals of operators acting on some families of sequence spaces ⋮ Ideals of operators on $(\oplus \ell ^\infty (n))_{\ell ^1}$ ⋮ Banach spaces for which the space of operators has 2^𝔠closed ideals ⋮ Some results on the lattice of closed ideals of $\mathcal L^r(X)$ for $X$ of the form $(\bigoplus_i \ell _p^i)_q$ ⋮ THE MAXIMAL IDEAL IN THE SPACE OF OPERATORS ON

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