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Moebius-invariant algebras in balls

Walter Rudin (1983)

Annales de l'institut Fourier

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 Ψ Y whenever f 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 (...).

Noncommutative function theory and unique extensions

David P. Blecher, Louis E. Labuschagne (2007)

Studia Mathematica

We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő L p -distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of H from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary...

Normed algebras of differentiable functions on compact plane sets: completeness and semisimple completions

Heiko Hoffmann (2011)

Studia Mathematica

We continue the study of the completeness and completions of normed algebras of differentiable functions Dⁿ(K) (where K is a perfect, compact plane set), initiated by Bland, Dales and Feinstein [Studia Math. 170 (2005) and Indian J. Pure Appl. Math. 41 (2010)]. We prove new characterizations of the completeness of D¹(K) and results concerning the semisimplicity of the completion of D¹(K). In particular, we prove that semi-rectifiability is necessary for the completion of D¹(K) to be semisimple in...

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