Invariant subspaces and closed ideals in banach spaces and algebras of functions

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Project objective

Research objectives and content The project lies in the border area between functional analysis and function theory and consists of two topics. Firstly, I will study the biinvariant subspaces of certain weighted spaces of functions on the circle. I expect either to obtain a characterization of these in terms of zero sets and inner factors or to show that a characterization in these terms is not possible. Secondly, I will investigate the closed ideals in non-separable Banach algebras of analytic functions on the unit disc with the main emphasis on the Lipschitz algebras. For these I expect to show that, given a certain set of conditions, there exists a smallest closed ideal which satisfies these. Moreover, I expect to give a Beurling-Rudin characterization of the weak-star closed ideals in these algebras. Training content (objective. benefit and expected impact) The main methods that will be used in the project are the weighted hyper-distributions and the Carleman transform. Prof. J. Esterle from the host institution is a leading expert in these techniques and, through the training, I expect to gain insight into how to apply them. Links with industry / industrial relevance (22)

Original text from CORDIS.

Participants

• UNIVERSITE DE BORDEAUX I · TALENCECoordinatorFrance
• Not availableCity levelDenmark

Links

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