Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Veröffentlicht
Spectrally starred advertibly complete A-p-normed algebras
Álgebras A-p-normadas espectralmente estrella completas
DOI:
https://doi.org/10.15446/recolma.v57n1.112430Schlagworte:
Q-normed algebra, Advertibly complete algebra, Starred spectrum, Spectrally convex algebra, Spectrally starred algebra, Jacobson's radical, Involutive algebra, Normal element, Unitary element (en)álgebra Q-normada,, espectro estrella, álgebra espectralmente convexa, álgebra espectral estrella, radical de Jacobson, álgebra involutiva, elemento normal, elemento unitario (es)
Downloads
We show that an advertibly complete A-p normed algebra E is isomorphic to the complex field C, modulo its radical, in any of the following cases: 1) every element of E has a star-shaped spectrum, 2) E is involutive and every normal element of E has a star-shaped spectrum; 3) E is hermitian and every unitary element of E has a star-shaped spectrum.
Probamos que un álgebra A-p-normada E advertible completa es isomorfa al campo complejo C, módulo su radical, si se da una de las siguientes condiciones: 1) todo elemento de E tiene espectro en forma estrella, 2) el álgebra E es involutiva y todo elemento normal de E tiene espectro en forma estrella; 3) el álgebra E es hermitiana and todo elemento unitario de E tiene espectro en forma estrella.
Literaturhinweise
B. Aupetit, A primer on spectral theory, Universitext. Springer-Verlag, New York, 1991. DOI: https://doi.org/10.1007/978-1-4612-3048-9
S. Bhatt, Spectrally convex Banach algebras, Indian J. Pure Appl. Math. 10 (1979), no. 6, 726-730.
F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, New York-Heidelberg, 1973. DOI: https://doi.org/10.1007/978-3-642-65669-9
I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418. DOI: https://doi.org/10.1215/S0012-7094-49-01640-3
A. Ouhmidou and A. El Kinani, On Spectrally convex ordinary algebras, Indian J. Pure Appl. Math. 53 (2022), no. 2, 349-354. DOI: https://doi.org/10.1007/s13226-021-00006-x
V. Pták, Banach algebras with involution, Manuscripta Math 6 (1972), 245-290. DOI: https://doi.org/10.1007/BF01304613
M. Roitman and Y. Sternfeld, When is a linear functional multiplicative?, Trans. Amer. Math. Soc. 267 (1981), no. 1, 111-124. DOI: https://doi.org/10.1090/S0002-9947-1981-0621976-6
S. Warner, Polynomial completeness in locally multiplicativelyconvex algebras, Duke Math. J. 23 (1956), 1-11. DOI: https://doi.org/10.1215/S0012-7094-56-02301-8
W. Z_ elazko, Selected topics in topological algebras, Lecture Notes Series, No. 31. Aarhus Universitet, Matematisk Institut, Aarhus, 1971, iii+176 pp.
