On norm closed ideals in L(pq)
Abstract
It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X=p (1 p < ∞) or X=c0 is the ideal of compact operators. The next natural question is to describe all closed ideals of L(pq) for 1 p,q < ∞, p ≠ q, or, equivalently, the closed ideals in L(p,q) for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in L(p,q), including one that has not been studied before. The proofs use various methods from Banach space theory.
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