Closed ideals in algebras of smooth functions

Hanin Leonid G.

Displaying similar documents to “Closed ideals in algebras of smooth functions”

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...

On norm closed ideals in $L (ℓ_{p}, ℓ_{q})$

B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)

Studia Mathematica

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It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for $X = ℓ_{p}$ (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L (ℓ_{p} \oplus ℓ_{q})$ for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in $L (ℓ_{p}, ℓ_{q})$ for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in $L (ℓ_{p}, ℓ_{q})$ , including one that has not been studied before. The proofs use various methods...

On the associated prime ideals of local cohomology modules defined by a pair of ideals

Maryam Jahangiri, Zohreh Habibi, Khadijeh Ahmadi Amoli (2016)

Discussiones Mathematicae General Algebra and Applications

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Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets $A s s_{R} (E x t_{R}^{n} (R / I, M))$ and $S u p p_{R} (E x t_{R}^{i} (R / I, H_{I, J}^{j} (M)))$ are finite for all i ≤ n+1 and all j < n, then so is $A s s_{R} (H o m_{R} (R / I, H_{I, J}^{n} (M)))$ . We also study the finiteness of $A s s_{R} (E x t_{R}^{i} (R / I, H_{I, J}^{n} (M)))$ for i = 1,2.

Semiproper ideals

Hiroshi Sakai (2005)

Fundamenta Mathematicae

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We say that an ideal I on $_{κ} λ$ is semiproper if the corresponding poset $ℙ_{I}$ is semiproper. In this paper we investigate properties of semiproper ideals on $_{κ} λ$ .

Non-regularity for Banach function algebras

J. Feinstein, D. Somerset (2000)

Studia Mathematica

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Let A be a unital Banach function algebra with character space $Φ_{A}$ . For $x \in Φ_{A}$ , let $M_{x}$ and $J_{x}$ be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of $J_{x}$ is connected, and that if x does not belong to the Shilov boundary of A then the set $y \in Φ_{A} : M_{x} \supseteq J_{y}$ has an infinite connected subset. Various related results are given.

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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Uniform spectral radius and compact Gelfand transform

Alexandru Aleman, Anders Dahlner (2006)

Studia Mathematica

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We consider the quantization of inversion in commutative p-normed quasi-Banach algebras with unit. The standard questions considered for such an algebra A with unit e and Gelfand transform x ↦ x̂ are: (i) Is $K_{ν} = s u p {| | (e - x)}^{- 1} {| |}_{p} {: x \in A, | | x | |}_{p} \leq 1, m a x | x ̂ | \leq ν$ bounded, where ν ∈ (0,1)? (ii) For which δ ∈ (0,1) is $C_{δ} = s u p | | x^{- 1} {| |}_{p} {: x \in A, | | x | |}_{p} \leq 1, m i n | x ̂ | \geq δ$ bounded? Both questions are related to a “uniform spectral radius” of the algebra, $r_{\infty} (A)$ , introduced by Björk. Question (i) has an affirmative answer if and only if $r_{\infty} (A) < 1$ , and this result is extended to more general nonlinear extremal...

Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

Jean Ludwig, Lyudmila Turowska (2006)

Studia Mathematica

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Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we...

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

Zenobia Anusiak (1971)

Colloquium Mathematicae

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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.

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...

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.

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

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

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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.

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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On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

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Schur Lemma and the Spectral Mapping Formula

Antoni Wawrzyńczyk (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let B be a complex topological unital algebra. The left joint spectrum of a set S ⊂ B is defined by the formula $σ_{l} (S)$ = ${(λ (s))}_{s \in S} \in ℂ^{S} | {s - λ (s)}_{s \in S}$ generates a proper left ideal $.$ Using the Schur lemma and the Gelfand-Mazur theorem we prove that $σ_{l} (S)$ has the spectral mapping property for sets S of pairwise commuting elements if (i) B is an m-convex algebra with all maximal left ideals closed, or (ii) B is a locally convex Waelbroeck algebra. The right ideal version of this result is also valid.

On the spectral radius in $L_{1} (G)$

E. Porada (1971)

Colloquium Mathematicae

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Spectral synthesis and operator synthesis

K. Parthasarathy, R. Prakash (2006)

Studia Mathematica

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Relations between spectral synthesis in the Fourier algebra A(G) of a compact group G and the concept of operator synthesis due to Arveson have been studied in the literature. For an A(G)-submodule X of VN(G), X-synthesis in A(G) has been introduced by E. Kaniuth and A. Lau and studied recently by the present authors. To any such X we associate a $V^{\infty} (G)$ -submodule X̂ of ℬ(L²(G)) (where $V^{\infty} (G)$ is the weak-* Haagerup tensor product $L^{\infty} (G) \otimes_{w * h} L^{\infty} (G)$ ), define the concept of X̂-operator synthesis and prove that a...

$0$ -ideals in $0$ -distributive posets

Khalid A. Mokbel (2016)

Mathematica Bohemica

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The concept of a $0$ -ideal in $0$ -distributive posets is introduced. Several properties of $0$ -ideals in $0$ -distributive posets are established. Further, the interrelationships between $0$ -ideals and $α$ -ideals in $0$ -distributive posets are investigated. Moreover, a characterization of prime ideals to be $0$ -ideals in $0$ -distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$ -ideal of a $0$ -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...