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Köthe coechelon spaces as locally convex algebras

José Bonet, Paweł Domański (2010)

Studia Mathematica

We study those Köthe coechelon sequence spaces k p ( V ) , 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra k p ( V ) is unital, locally m-convex, a -algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals...

Mittag-Leffler methods in analysis.

Jorge Mújica (1995)

Revista Matemática de la Universidad Complutense de Madrid

In this survey we present two Mittag-Leffler lemmas and several applications to topics as varied as the delta-equation, Fréchet algebras, inductive limits of Banach spaces and quasi-normable Fréchet spaces.

Multiplicative functionals and entire functions

Krzysztof Jarosz (1996)

Studia Mathematica

Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.

Multiplicative functionals and entire functions, II

Krzysztof Jarosz (1997)

Studia Mathematica

Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.

On joint spectral radii in locally convex algebras

Andrzej Sołtysiak (2006)

Studia Mathematica

We present several notions of joint spectral radius of mutually commuting elements of a locally convex algebra and prove that all of them yield the same value in case the algebra is pseudo-complete. This generalizes a result proved by the author in 1993 for elements of a Banach algebra.

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