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Some simple proofs in holomorphic spectral theory

100%

Allan G.

Banach Center Publications

2007

tom 75

nr 1

9-15

This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.

An analytic approach to the spectral characterization of the radical

100%

Allan G.

Studia Mathematica

2008

tom 186

nr 1

11-14

We give a simple complex-variable proof of an old result of Zemánek and Le Page on the radical of a Banach algebra. Incidentally, the argument also proves a recent result of Harris and Kadison.

Elements of finite closed descent in Banach and Fréchet algebras

100%

Allan G.

Banach Center Publications

2005

tom 67

nr 1

73-81

This paper will give a brief survey of ideas related to 'elements of finite closed descent' in certain kinds of topological algebra.

Ograniczanie wyników

2 Banach Center Publications

1 Studia Mathematica

3 Allan G.

1 2008

1 2007

1 2005

Wyniki wyszukiwania

Some simple proofs in holomorphic spectral theory

An analytic approach to the spectral characterization of the radical

Elements of finite closed descent in Banach and Fréchet algebras