Displaying similar documents to “Banach-Stone Theorems for Banach Manifolds.”

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

Frontisi, Julien (1996)

Serdica Mathematical Journal

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It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

Multiplicative functionals on algebras of differentiable functions.

Jesús A. Jaramillo (1990)

Extracta Mathematicae

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Let Ω be an open subset of a real Banach space E and, for 1 ≤ m ≤, let C(Ω) denote the algebra of all m-times continuously Fréchet differentiable real functions defined on Ω. We are concerned here with the question as to wether every nonzero algebra homomorphism φ: C(Ω) → R is given by evaluation at some point of Ω, i.e., if there exists some a ∈ Ω such that φ(f) = f(a) for each f ∈ C(Ω). This problem has been considered in [1,4,5] and [6]. In [6], a positive answer is given in the case...

Homomorphisms on some function algebras.

M.ª Isabel Garrido, Javier Gómez Gil, Jesús Angel Jaramillo (1992)

Extracta Mathematicae

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Suppose that A is an algebra of continuous real functions defined on a topological space X. We shall be concerned here with the problem as to whether every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X, in the sense that there exists some a in X such that φ(f) = f(a) for every f in A. The problem goes back to the work of Michael [19], motivated by the question of automatic continuity of homomorphisms in a symmetric *-algebra. More recently, the problem...

Banach's school and topological algebras

Wiesław Żelazko (2009)

Banach Center Publications

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We present here some evidence of the activity of Banach Lwów School of functional analysis in the field of topological algebras. We shall list several results connected with such names as Stanisław Mazur (1905-1981), Maks (Meier) Eidelheit (1910-1943), Stefan Banach (1892-1945) and Andrzej Turowicz (1904-1989) showing that if the war had not interrupted this activity we could expect more interesting results in this direction.