Pseudo-Banach algebras

Allan, Graham; Dales, H. G.; McClure, J. P.

doi:10.4064/sm-40-1-55-69

Cited by 30 publications

(54 citation statements)

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“…Soit U un ouvert de C' 1 , désignons par d la distance au bord de U : d{s) = dist (s, [ U). J. P. Ferrier [8] et P. Pflug [14] ont remarqué que la thèse d'L Cnop [5] ou [6] permet d'améliorer le résultat du type « théorème de la couronne » de L. Hôrmander [12] :…”

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Calcul fonctionnel dépendant de la croissance des coefficients spectraux

Nguyen¹

1977

Annales De L’institut Fourier

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Calcul fonctionnel dépendant de la croissance des coefficients spectraux

Nguyen¹

1977

Annales De L’institut Fourier

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“…Iii particular, every element ob sucit an algebra-is regular (bounded of [2]), tite spectrurn ob an element ob a pseudo-complete uíibarrnly A-coívex algebra E is compact, anO ib E is loca-Uy complete, it 18 a-pseuda-Baiacit álgebra-u tite seise ob [3] or a 1... Oubbi complete b.m.c.a-. in tite sense ob [1] a-nO [6].…”

Section: ¡F E 13 Pseudo-cornplete It Is a Direeted Union Of Banacit mentioning

confidence: 99%

Representation of Locally Convex Algebras

Oubbi¹

1994

Rev. Mat. Complut.

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ABSTRACT. We deal with the representation of locally convex algebras.On one hand as "suhalgebras" of sorne weighted space CV(X) anO on the other hand, in the case ob uniborrnly A-convex algebras, as inductive lirnits of Banach algebras. We amo study sorne questions on the spectrurn of a locally convex algebra. INTROD1JCTIONA locally convex algebra is an algebra togetber with a Hausdorff loca-fly convex topology such tha-t tite midtiplication ob E is sepa-rately continuous. We denote by M (resp. M#) the assumed nonvoid set ob a-II continuous (resp. a-lgebra-ic) citaracters of E. Endowed witit tite weak topology generated by E, M anO M# are Ha-usdorff completely regular spaces. M will be calleO tite spectrum ob E a-nO M# its algebraic spectrurn. Titis work consists obthree indepenOant sections. In [9], conditions are given under witich E is embedded aigebraicaily (anO topologica-lIy) in sorne (7(X) with tite compa-ct open topology or a-weaker topology. A.C. Cocitran sitows iii [4] titat every semisimple uniformly A-convex algebra E can be embedded continuously, via tite Gelba-nd ma-p

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“…Let E be as in §1. Now, A denotes a commutative complete multiplicatively convex bornological algebra [11], named pseudo-Banach in [1], with unity e. Essentially, A is the algebraic inductive limit of Banach algebras {A¿}je/, A = hjiiA¿, and its bounded sets are those contained and bounded in some A». Many algebras of functions, of germs of functions, of operators, the p-Banach algebras, the topological algebras with continuous inverse are of this kind.…”

Section: Proof Let ¡P Be a Morphism Verifying (I) And (Ii) Lef / G mentioning

confidence: 99%

Unicity of a holomorphic functional calculus in infinite dimensions

Galé¹

1986

Trans. Amer. Math. Soc.

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ABSTRACT. L. Waelbroeck gives a holomorphic functional calculus for Banach algebras and analytic functions on Banach spaces. The properties of this calculus extend the well-known properties for the case of several complex variables. In this last situation, W. Zame has obtained a theorem of unicity where the famous condition of compatibility is dropped. We obtain a theorem analogous to Zame's for Waelbroeck's calculus restricted to a certain algebra of germs of functions. We consider Banach spaces whose topological duals have the bounded approximation property. Also, results of the same kind as above are given for bornological algebras.

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Pseudo-Banach algebras

Cited by 30 publications

References 0 publications

Calcul fonctionnel dépendant de la croissance des coefficients spectraux

Calcul fonctionnel dépendant de la croissance des coefficients spectraux

Representation of Locally Convex Algebras

Unicity of a holomorphic functional calculus in infinite dimensions

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