Classifcation of closed ideals in the Banach algebra of bounded linear operators on a Banach space

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• Niels Jakob Laustsen (Lancaster)
• Wednesday 20 January 2010, 16:00-17:00
• Watson Building, LRA.

If you have a question about this talk, please contact Neal Bez.

Throughout mathematics, a fundamental problem is to understand the “building blocks” of a given object – for instance, number theorists study prime numbers, group theorists classify the normal subgroups of their favourite group, while ring theorists investigate the ideals of any new ring they meet. In Banach algebras, where the algebra in question carries a topology, the counterpart of this problem is to classify the closed ideals. We are interested in this problem for the class of Banach algebras of the form B(E), that is, all bounded linear operators on a Banach space E. Despite the fundamental nature of this problem, the list of Banach spaces E for which a complete classification of the closed ideals in B(E) has been achieved is very short indeed.

In the talk I shall present the full list and its history, and I shall outline ongoing work aimed at adding more spaces to this list.

This talk is part of the Analysis seminar series.

This talk is included in these lists:

• Analysis seminar
• Analysis seminar
• School of Mathematics events
• Watson Building, LRA

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