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On noncompact perturbation of nonconvex sweeping process

Myelkebir Aitalioubrahim (2012)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.

On norm closed ideals in L ( p , q )

B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)

Studia Mathematica

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 ( 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...

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