Bounded structures of uniformly A-convex algebras.
Oudadess, Mohamed (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Oudadess, Mohamed (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Mohamed Oudadess (1990)
Publicacions Matemàtiques
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Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.
L. Oubbi (1994)
Revista Matemática de la Universidad Complutense de Madrid
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We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.
W. Żelazko (1996)
Studia Mathematica
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We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
Jorma Arhippainen (1995)
Publicacions Matemàtiques
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Let A be an algebra over the field of complex numbers with a (Hausdorff) topology given by a family Q = {q|λ ∈ Λ} of square preserving r-homogeneous seminorms (r ∈ (0, 1]). We shall show that (A, T(Q)) is a locally m-convex algebra. Furthermore we shall show that A is commutative.
Susanne Dierolf, Thomas Heintz (2003)
RACSAM
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We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.
Nguyen Van Khue (1987)
Colloquium Mathematicae
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W. Żelazko (1963)
Studia Mathematica
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Kyriazis, Athanasios (1989)
Portugaliae mathematica
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KHIN AYE AYE AND KARL-HEINZ SCHRODER SUSANNE DiEROLF (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Iván Ezequiel Angiono (2015)
Journal of the European Mathematical Society
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We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko’s theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
Antoine Delcroix, Maximilian F. Hasler, Stevan Pilipović, Vincent Valmorin
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We give a description of various algebras of generalized functions based on the introduction of pseudo-ultranorms on spaces of sequences in given locally convex function algebras. We study sheaf properties of these algebras, needed for microlocal analysis, and also consider regularity theory, functoriality and different concepts of association and weak equality in a unified setting. Using this approach, we also give new results on embeddings of ultradistribution and hyperfunction spaces...