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Caracterisations de certaines algèbres de Banach par le calcul fonctionnel

A. Akkar, Abdellah El Kinani, M. Oudadess (1989)

Extracta Mathematicae

We show that the Banach algebras with continuous involution are the Banach algebras which admit a harmonic functional calculus, while we prove that the hermitian commutative Banach algebras are exactly the involutive commutative Banach algebras that admit a real analytic functional calculus.

Concerning entire functions in B 0 -algebras

W. Żelazko (1994)

Studia Mathematica

We construct a non-m-convex non-commutative B 0 -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

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.

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