Centralizers for subsets of normed algebras

Bertram Yood

Displaying similar documents to “Centralizers for subsets of normed algebras”

$ω$ -compact elements of normed algebras

Gh. Constantin (1973)

Matematički Vesnik

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$L_{1}$ contains every two-dimensional normed space

David Yost (1988)

Annales Polonici Mathematici

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A theorem on isotropic spaces

Félix Cabello Sánchez (1999)

Studia Mathematica

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Let X be a normed space and $G_{F} (X)$ the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if $G_{F} (X)$ acts transitively on the unit sphere then X must be an inner product space.

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

Zenobia Anusiak (1971)

Colloquium Mathematicae

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

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{s g}, I^{s g})$ and $(Q^{g}, I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K Q^{s g} / ⟨ I^{s g} ⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K Q^{g} / ⟨ I^{g} ⟩$ . As a corollary, we find that $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

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

Philip Olin (1975)

Colloquium Mathematicae

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On area and side lengths of triangles in normed planes

Gennadiy Averkov, Horst Martini (2009)

Colloquium Mathematicae

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Let $ℳ^{d}$ be a d-dimensional normed space with norm ||·|| and let B be the unit ball in $ℳ^{d}$ . Let us fix a Lebesgue measure $V_{B}$ in $ℳ^{d}$ with $V_{B} (B) = 1$ . This measure will play the role of the volume in $ℳ^{d}$ . We consider an arbitrary simplex T in $ℳ^{d}$ with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of $V_{B} (T)$ are determined. For d ≥ 3 it is noticed that the tight lower bound of $V_{B} (T)$ is zero.

Markov's property for kth derivative

Mirosław Baran, Beata Milówka, Paweł Ozorka (2012)

Annales Polonici Mathematici

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Consider the normed space $(ℙ (ℂ^{N}), | | \cdot | |)$ of all polynomials of N complex variables, where || || a norm is such that the mapping $L_{g} : (ℙ (ℂ^{N}), | | \cdot | |) ∋ f \mapsto g f \in (ℙ (ℂ^{N}), | | \cdot | |)$ is continuous, with g being a fixed polynomial. It is shown that the Markov type inequality $| \partial / \partial z_{j} {P | | \leq M (d e g P)}^{m} | | P | |$ , j = 1,...,N, $P \in ℙ (ℂ^{N})$ , with positive constants M and m is equivalent to the inequality $| | \partial^{N} / \partial z ₁ . . . \partial z_{N} P | | \leq M^{'} {(d e g P)}^{m^{'}} | | P | |$ , $P \in ℙ (ℂ^{N})$ , with some positive constants M’ and m’. A similar equivalence result is obtained for derivatives of a fixed order k ≥ 2, which can be more specifically formulated in the language of normed algebras....

$A F$ -algebras and topology of mapping tori

Igor Nikolaev (2015)

Czechoslovak Mathematical Journal

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The paper studies applications of $C^{*}$ -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of $A F$ -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding $A F$ -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension $2$ , $3$ and $4$ . In conclusion, we consider two numerical examples illustrating our main results.

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.

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...

A generalization of a formalized theory of fields of sets on non-classical logics

Helena Rasiowa

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Contents Introduction.................................................................................................................................................. 3 § 1. System $𝒮$ of a propositional calculus...................................................................... 4 § 2. System $𝒮 *$ ..................................................................................................................... 5 § 3. $𝒮 *$ -algebras.....................................................................................................................