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Continuity of generalized inverses in Banach algebras

Steffen Roch, Bernd Silbermann (1999)

Studia Mathematica

The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.

Continuity of the Drazin inverse II

J. Koliha, V. Rakočević (1998)

Studia Mathematica

We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.

Continuity versus boundedness of the spectral factorization mapping

Holger Boche, Volker Pohl (2008)

Studia Mathematica

This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.

Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras

Bruce Barnes (1995)

Studia Mathematica

The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.

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