On norm closed ideals in L(l p ,l q ) Academic Article

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 = c o is the ideal of compact operators. The next natural question is to describe all closed ideals of L(p q) 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. Instytut Matematyczny PAN, 2007.

authors

• Schlumprecht, Thomas

published proceedings

• Studia Mathematica

author list (cited authors)

• Sari, B., Schlumprecht, T. h., Tomczak-Jaegermann, N., & Troitsky, V. G.

citation count

• 20

complete list of authors

• Sari, B||Schlumprecht, Th||Tomczak-Jaegermann, N||Troitsky, VG

publication date

• July 2007

publisher

• Institute of Mathematics, Polish Academy of Sciences  Publisher

published in

• Studia Mathematica  Journal

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.4064/sm179-3-3

start page

• 239

end page

• 262

volume

• 179

issue

• 3

URL

• http://dx.doi.org/10.4064/sm179-3-3