Approximate identities for Ideals in $L(L^p))$

William B. Johnson, Gideon Schechtman

Type: Preprint

Publication Date: 2024-02-20

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2402.13438

Abstract

The main result is that the only non trivial closed ideal in the Banach algebra $L(L^p)$ of bounded linear operators on $L^p(0,1)$, $1\le p < \infty$, that has a left approximate identity is the ideal of compact operators. The algebra $L(L^1)$ has at least one non trivial closed ideal that has a contractive right approximate identity as well as many, including the unique maximal ideal, that do not have a right approximate identity.

Locations

arXiv (Cornell University) - View - PDF

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