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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.

On linear extension for interpolating sequences

Eric Amar (2008)

Studia Mathematica

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces H p ( σ ) and the H p ( σ ) interpolating sequences S in the p-spectrum p of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is H s ( σ ) -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in H ( ) then S is H p ( ) -interpolating with a linear...

On locally pseudoconvexes square algebras.

Jorma Arhippainen (1995)

Publicacions Matemàtiques

Let A be an algebra over the field of complex numbers with a (Hausdorff) topology given by a family Q = {qλ|λ ∈ Λ} of square preserving rλ-homogeneous seminorms (rλ ∈ (0, 1]). We shall show that (A, T(Q)) is a locally m-convex algebra. Furthermore we shall show that A is commutative.

On multiplication in spaces of continuous functions

Marek Balcerzak, Aleksander Maliszewski (2011)

Colloquium Mathematicae

We introduce and examine the notion of dense weak openness. In particular we show that multiplication in C(X) is densely weakly open whenever X is an interval in ℝ.

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