Displaying similar documents to “Schwartz kernel theorem in algebras of generalized functions”

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety 𝐊 ̲ 2 by means of K ̲ 2 -quadruples. We also characterize isomorphisms of these algebras by means of K ̲ 2 -quadruples.

Generalized Post algebras and their application to some infinitary many-valued logics

Cat-Ho Nguyen

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CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7   1. Definition and characterization of generalized Post algebras............................................. 7   2. Post...

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

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We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra ^ ( M ) on the manifold M given in [gksv].

Metric generalizations of Banach algebras

W. Żelazko

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CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2

Bruce Allison, Stephen Berman, Arturo Pianzola (2014)

Journal of the European Mathematical Society

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Let 𝕄 n be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n -tuples of commuting finite order automorphisms. It is a classical result that 𝕄 1 is the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in 𝕄 1 . In this paper, we classify the algebras in 𝕄 2 , and further determine the relationship between...

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

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In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for A = U 0 M V , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and V M is a good V-module.

Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

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For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras A p ( G , ω ) . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We...

Some remarks on Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that p , ( 1 p ) are Q algebras and that A n = L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .

Deformed mesh algebras of Dynkin type ℂₙ

Jerzy Białkowski, Karin Erdmann, Andrzej Skowroński (2012)

Colloquium Mathematicae

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In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type 2 n . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable...

A new proof of the noncommutative Banach-Stone theorem

David Sherman (2006)

Banach Center Publications

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Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate...

Local derivations for quotient and factor algebras of polynomials

Andrzej Nowicki, Ilona Nowosad (2003)

Colloquium Mathematicae

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We describe all Kadison algebras of the form S - 1 k [ t ] , where k is an algebraically closed field and S is a multiplicative subset of k[t]. We also describe all Kadison algebras of the form k[t]/I, where k is a field of characteristic zero.

Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

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We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where A = p for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras p ( ω ) .

Monadic n × m -valued Łukasiewicz-Moisil algebras

A. V. Figallo, Claudia A. Sanza (2012)

Mathematica Bohemica

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Here we initiate an investigation into the class m L M n × m of monadic n × m -valued Łukasiewicz-Moisil algebras (or m L M n × m -algebras), namely n × m -valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic n -valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that m L M n × m is a discriminator variety and as a consequence,...

Annihilators in BCK-algebras

Radomír Halaš (2003)

Czechoslovak Mathematical Journal

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We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra 𝒜 . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice 𝒟 ( A ) of all deductive systems on 𝒜 . Moreover, relative annihilators of C 𝒟 ( A ) with respect to B 𝒟 ( A ) are introduced and serve as relative pseudocomplements of C w.r.t. B in 𝒟 ( A ) .