Abstract
We study the lattice of closed ideals in the algebra of continuous linear operators acting on pth Tandori and \(p'\)th Cesàro sequence spaces, \(1\leqslant p<\infty \), which we show are isomorphic to the classical sequence spaces \((\oplus _{n=1}^\infty \ell _\infty ^n)_p\) and \((\oplus _{n=1}^\infty \ell _1^n)_{p'}\), respectively. We also show that Tandori sequence spaces are complemented in certain Lorentz sequence spaces, and that the lattice of closed ideals for certain other Lorentz and Garling sequence spaces has infinite cardinality.
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The author thanks an anonymous referee for his valuable suggestions on improving this paper.
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Communicated by Mikhail Ostrovskii.
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Wallis, B. Closed ideals of operators acting on some families of sequence spaces. Banach J. Math. Anal. 14, 98–115 (2020). https://doi.org/10.1007/s43037-019-00026-0
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DOI: https://doi.org/10.1007/s43037-019-00026-0