Köthe coechelon spaces as locally convex algebras

José Bonet; Paweł Domański

Displaying similar documents to “Köthe coechelon spaces as locally convex algebras”

Closed ideals in algebras of smooth functions

Hanin Leonid G.

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AbstractA topological algebra admits spectral synthesis of ideals (SSI) if every closed ideal in this algebra is an intersection of closed primary ideals. According to classical results this is the case for algebras of continuous, several times continuously differentiable, and Lipschitz functions. New examples (and counterexamples) of function algebras that admit or fail to have SSI are presented. It is shown that the Sobolev algebra $W_{p}^{l} (ℝ ⁿ)$ , 1 ≤ p < ∞, has the property of SSI for and only...

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§...

Dual complementors in topological algebras

Marina Haralampidou (2005)

Banach Center Publications

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We deal with dual complementors on complemented topological (non-normed) algebras and give some characterizations of a dual pair of complementors for some classes of complemented topological algebras. The study of dual complementors shows their deep connection with dual algebras. In particular, we refer to Hausdorff annihilator locally C*-algebras and to proper Hausdorff orthocomplemented locally convex H*-algebras. These algebras admit, by their nature, the same type of dual pair of...

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...

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 ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

A property for locally convex *-algebras related to property (T) and character amenability

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

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For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let $C_{c} (G)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $(C_{c} (G), ε_{G})$ has property (FH) if and only if G has property...

Generalization of the topological algebra $(C_{b} (X), β)$

Jorma Arhippainen, Jukka Kauppi (2009)

Studia Mathematica

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We study subalgebras of $C_{b} (X)$ equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.

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...

Second duals of measure algebras

H. G. Dales, A. T.-M. Lau, D. Strauss

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Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L¹(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C₀(Ω)” of the C*-algebra C₀(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω. We shall study the C*-algebra $B^{b} (Ω)$ of bounded Borel functions on Ω, and we shall determine the exact cardinality of a variety...

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 $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , 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.

Erratum to “Can $ℬ (ℓ^{p})$ ever be amenable?” (Studia Math. 188 (2008), 151-174)

Matthew Daws, Volker Runde (2009)

Studia Mathematica

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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 $\hat{} (M)$ on the manifold M given in [gksv].

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

On m-convex $B_{0}$ -algebras of type ES

W. Żelazko (1969)

Colloquium Mathematicae

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Noncommutative function theory and unique extensions

David P. Blecher, Louis E. Labuschagne (2007)

Studia Mathematica

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We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő $L^{p}$ -distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of $H^{\infty}$ from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and...

Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{matrix} F_{m}^{1} \end{matrix}$ nilradical

L.M. Camacho, B.A. Omirov, K.K. Masutova, I.M. Rikhsiboev (2017)

Open Mathematics

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All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras

Christian Kassel (2013)

Annales mathématiques Blaise Pascal

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We define polynomial $H$ -identities for comodule algebras over a Hopf algebra $H$ and establish general properties for the corresponding $T$ -ideals. In the case $H$ is a Taft algebra or the Hopf algebra $E (n)$ , we exhibit a finite set of polynomial $H$ -identities which distinguish the Galois objects over $H$ up to isomorphism.

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 $A = ℓ^{p}$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras $ℓ^{p} (ω)$ .

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...

Stronger ideals over $_{κ} λ$

Yo Matsubara (2002)

Fundamenta Mathematicae

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In §1 we define some properties of ideals by using games. These properties strengthen precipitousness. We call these stronger ideals. In §2 we show some limitations on the existence of such ideals over $_{κ} λ$ . We also present a consistency result concerning the existence of such ideals over $_{κ} λ$ . In §3 we show that such ideals satisfy stronger normality. We show a cardinal arithmetical consequence of the existence of strongly normal ideals. In § 4 we study some “large cardinal-like” consequences...

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

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A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{\infty}$ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

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On some spaces of linear functionals on the algebras $A_{p} (G)$ for locally compact groups

E. E. Granirer (1987)

Colloquium Mathematicae

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On domains with ACC on invertible ideals

Stefania Gabelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_{m}(A)$ of maximal invertible ideals. In this note we study some properties of $I_{m}(A)$ and we prove that, if $I(A)$ is a free group on $I_{m}(A)$ , then $A$ is a locally factorial Krull domain.