Abstract of a paper by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, and V.G. Troitsky
This is an announcement for the paper "On norm closed ideals in L(\ell_p\oplus\ell_q)" by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, and V.G. Troitsky. Abstract: It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0 is the ideal of compact operators. The next natural question is to describe all closed ideals of L(\ell_p\oplus\ell_q) for 1 \le p,q < \infty, p \neq q, or, equivalently, the closed ideals in L(\ell_p,\ell_q) for p < q. This paper shows that for 1 < p < 2 < q < \infty there are at least four distinct proper closed ideals in L(\ell_p,\ell_q), including one that has not been studied before. The proofs use various methods from Banach space theory. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 47L20; 47B10; 47B37 Remarks: 24 pages Submitted from: vtroitsky@math.ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0509414 or http://arXiv.org/abs/math.FA/0509414 or by email in unzipped form by transmitting an empty message with subject line uget 0509414 or in gzipped form by using subject line get 0509414 to: math@arXiv.org.
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Dale Alspach