EuDML | Browse

It is proved that the Fréchet algebra $C (B)$ has exactly three closed subalgebras $Y$ which contain nonconstant functions and which are invariant, in the sense that $f \circ Ψ \in Y$ whenever $f \in Y$ and $Ψ$ is a biholomorphic map of the open unit ball $B$ of $C^{n}$ onto $B$ . One of these consists of the holomorphic functions in $B$ , the second consists of those whose complex conjugates are holomorphic, and the third is $C (B)$ .

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.

Multiplicative functionals on algebras of differentiable functions.

Jesús A. Jaramillo (1990)

Extracta Mathematicae

Let Ω be an open subset of a real Banach space E and, for 1 ≤ m ≤, let Cm(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: Cm(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 ∈ Cm(Ω). This problem has been considered in [1,4,5] and [6]. In [6], a positive answer is given in the case that...

Multiplicative structure of de Branges's spaces.

Benjamin A. Lotto, Donald Sarason (1991)

Revista Matemática Iberoamericana

L. de Branges has originated a viewpoint one of whose repercussions has been the detailed analysis of certain Hilbert spaces of holomorphic functions contained within the Hardy space H2 of the unit disk (...).

Displaying 1 – 12 of 12

Currently displaying 1 – 12 of 12