Weak multiplicative operators on function algebras without units

Thomas Tonev

Displaying similar documents to “Weak multiplicative operators on function algebras without units”

Algebra isomorphisms between standard operator algebras

Thomas Tonev, Aaron Luttman (2009)

Studia Mathematica

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If X and Y are Banach spaces, then subalgebras ⊂ B(X) and ⊂ B(Y), not necessarily unital nor complete, are called standard operator algebras if they contain all finite rank operators on X and Y respectively. The peripheral spectrum of A ∈ is the set $σ_{π} (A) = λ \in σ (A) : | λ | = m a x_{z \in σ (A)} | z |$ of spectral values of A of maximum modulus, and a map φ: → is called peripherally-multiplicative if it satisfies the equation $σ_{π} (φ (A) \circ φ (B)) = σ_{π} (A B)$ for all A,B ∈ . We show that any peripherally-multiplicative and surjective map φ: → , neither assumed to be...

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...

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...

Engel BCI-algebras: an application of left and right commutators

Ardavan Najafi, Arsham Borumand Saeid (2021)

Mathematica Bohemica

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We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of $n$ -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type $2$ is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is...

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§...

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.

Generators for algebras dense in $L^{p}$ -spaces

Alexander J. Izzo, Bo Li (2013)

Studia Mathematica

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For various $L^{p}$ -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in $L^{p} (μ)$ . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function...

Almost multiplicative functions on commutative Banach algebras

S. H. Kulkarni, D. Sukumar (2010)

Studia Mathematica

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Let A be a complex commutative Banach algebra with unit 1 and δ > 0. A linear map ϕ: A → ℂ is said to be δ-almost multiplicative if |ϕ(ab) - ϕ(a)ϕ(b)| ≤ δ||a|| ||b|| for all a,b ∈ A. Let 0 < ϵ < 1. The ϵ-condition spectrum of an element a in A is defined by $σ_{ϵ} (a) : = λ \in ℂ : | | λ - {a | | | | (λ - a)}^{- 1} | | \geq 1 / ϵ$ with the convention that $| | λ - {a | | | | (λ - a)}^{- 1} | | = \infty$ when λ - a is not invertible. We prove the following results connecting these two notions: (1) If ϕ(1) = 1 and ϕ is δ-almost multiplicative, then $ϕ (a) \in σ_{δ} (a)$ for all a in A. (2) If ϕ is linear and $ϕ (a) \in σ_{ϵ} (a)$ for...

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...

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

Zenobia Anusiak (1971)

Colloquium Mathematicae

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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...

$ω$ -compact elements of normed algebras

Gh. Constantin (1973)

Matematički Vesnik

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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.

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

Philip Olin (1975)

Colloquium Mathematicae

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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 $ℓ^{p} (ω)$ .

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

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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Centralizers for subsets of normed algebras

Bertram Yood (2000)

Studia Mathematica

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Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either $c x c^{- 1} = x$ for all c ∈ H or $s u p ∥ c x c^{- 1} ∥ : c \in H = \infty$ . In that case the set of x ∈ A for which the sup is finite is the centralizer of H.