### Continuity of spectrum and spectral radius in algebras of operators

Laura Burlando (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Laura Burlando (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Robin Harte (1996)

Studia Mathematica

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An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.

Laura Burlando (1994)

Banach Center Publications

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This survey deals with necessary and/or sufficient conditions for continuity of the spectrum and spectral radius functions at a point of a Banach algebra.

Seán Dineen (1970)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Dietmar Abts (1980)

Commentationes Mathematicae Universitatis Carolinae

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L. Waelbroeck (1982)

Banach Center Publications

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Christoph Schmoeger (1995)

Studia Mathematica

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A bounded linear operator T on a complex Banach space X is called an operator of Saphar type if its kernel is contained in its generalized range ${\bigcap}_{n=1}^{\infty}{T}^{n}\left(X\right)$ and T is relatively regular. For T of Saphar type we determine the supremum of all positive numbers δ such that T - λI is of Saphar type for |λ| < δ.