# Multiplicative functionals on algebras of differentiable functions.

Extracta Mathematicae (1990)

- Volume: 5, Issue: 3, page 144-146
- ISSN: 0213-8743

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topJaramillo, Jesús A.. "Multiplicative functionals on algebras of differentiable functions.." Extracta Mathematicae 5.3 (1990): 144-146. <http://eudml.org/doc/39896>.

@article{Jaramillo1990,

abstract = {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 m < ∞ and E is a Banach space which admits Cm-partitions of unity and with nonmeasurable cardinal; this result is obtained there as a by-product of the study of two topologies, and , introduces on Cm(Ω). In [1] (respectively, in [4]) a positive answer is given in the case that Ω = E is a separable Banach space (respectively, the dual of a separable Banach space). In the present note we extend these previous results, and we give an affirmative answer for a wider class of Banach spaces, including super-reflexive spaces with nonmeasurable cardinal. We also provide a direct approach and a unified treatment, since our results here are derived as a consequence of Theorem 1 below, a general result slightly in the spirit of Theorem 12.5 of [7].},

author = {Jaramillo, Jesús A.},

journal = {Extracta Mathematicae},

keywords = {Algebra de funciones; Anillos de funciones; Funcional lineal; Multiplicadores; Homomorfismos; Algebra topológica; homomorphism; point evaluation; algebras of differentiable functions; super-reflexive Banach spaces with nonmeasurable cardinal},

language = {eng},

number = {3},

pages = {144-146},

title = {Multiplicative functionals on algebras of differentiable functions.},

url = {http://eudml.org/doc/39896},

volume = {5},

year = {1990},

}

TY - JOUR

AU - Jaramillo, Jesús A.

TI - Multiplicative functionals on algebras of differentiable functions.

JO - Extracta Mathematicae

PY - 1990

VL - 5

IS - 3

SP - 144

EP - 146

AB - 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 m < ∞ and E is a Banach space which admits Cm-partitions of unity and with nonmeasurable cardinal; this result is obtained there as a by-product of the study of two topologies, and , introduces on Cm(Ω). In [1] (respectively, in [4]) a positive answer is given in the case that Ω = E is a separable Banach space (respectively, the dual of a separable Banach space). In the present note we extend these previous results, and we give an affirmative answer for a wider class of Banach spaces, including super-reflexive spaces with nonmeasurable cardinal. We also provide a direct approach and a unified treatment, since our results here are derived as a consequence of Theorem 1 below, a general result slightly in the spirit of Theorem 12.5 of [7].

LA - eng

KW - Algebra de funciones; Anillos de funciones; Funcional lineal; Multiplicadores; Homomorfismos; Algebra topológica; homomorphism; point evaluation; algebras of differentiable functions; super-reflexive Banach spaces with nonmeasurable cardinal

UR - http://eudml.org/doc/39896

ER -

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