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3 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

3 Łuczak M.

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A characterization of linear-multiplicative functionals in topological algebras

Łuczak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

79-91

The classical Gleason–Kahane–Zelazko theorem for complex Banach algebras was generalized for not necessary linear functionals by Kowalski and Słodkowski. We prove a version of the Kowalski–Słodkowski theorem for real Banach algebras and also for real and complex A-pseudoconvex algebras.

Holomorphic functional calculus in A-pseudoconvex algebras

Łuczak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 2

161--169

We Defie and study a holomorphic functional calculus for a single element In complex and real complete A-pseudoalgebras with unit. As a consequence of the main result we obtain the spectral mapping theorem and existence of the logarithm and the nth root of an algebra element.

On the Gleason-Kahane-Żelazko theorem

Łuczak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 2

245-253

We prove a generalisation of the Gleason-Kahane-Żelazko theorem in real Banach algebras with unit. We also prove the classical Gleason-Kahane-Żelazko theorem in strictly real algebras with unit in which the spectrum of every element is bounded, and (for continuous functionals) in real and complex A-pseudoconvex algebras with unit.