جستجوی مقالات مرتبط با کلیدواژه « c ∗ -algebra » در نشریات گروه « ریاضی »

For a locally compact group $G$ and $p\in(1,\infty)$, let $B_p(G)$ is the multiplier algebra of the Fig\`{a}-Talamanca-Herz algebra $A_p(G)$. For $p=2$ and $G$ amenable, the algebra $B(G):= B_2(G)$ is the usual Fourier-Stieltjes algebra. In this paper, we show that $A_p(G)$ is a Bochner-Schoenberg-Eberlin (BSE) algebra and every clopen subset of $G$ is a synthetic set for $A_p(G)$. Furthermore, we characterize idempotent elements of the Banach algebra $B_p(G)$. This result generalizes the Cohen-Host idempotent theorems for the case of Fig\`{a}-Talamanca-Herz algebras. Characterization of idempotent elements of $B_p(G)$ is of paramount importance to study homomorphisms in Fig\`{a}-Talamanca-Herz algebras.

We study the two-stage stochastic infinity norm optimization problem with recourse based on a commutative algebra. First, we explore and develop the algebraic structure of the infinity norm cone, and utilize it to compute the derivatives of the barrier recourse functions. Then, we prove that the barrier recourse functions and the composite barrier functions for this optimization problem are self-concordant families with reference to barrier parameters. These findings are used to develop interior-point algorithms based on primal decomposition for this class of stochastic programming problems. Our complexity results for the short- and long-step algorithms show that the dominant complexity terms are linear in the rank of the underlying cone. Despite the asymmetry of the infinity norm cone, we also show that the obtained complexity results match (in terms of rank) the best known results in the literature for other well-studied stochastic symmetric cone programs. Finally, we demonstrate the efficiency of the proposed algorithm by presenting some numerical experiments on both stochastic uniform facility location problems and randomly-generated problems.

‎‎‎‎‎In this paper, we define a new concept called ``strongly orthogonality preserving mappings '' for inner product modules, which extends the existing notion of ``orthogonality preserving mappings". Also, we provide a condition that is both necessary and sufficient for a linear map between inner product modules to be strongly orthogonality preserving. Some examples on the definition are given.

In this paper, we introduce a special types of Z−ideals in MV −algebras and delve into theirproperties. These particular ideals are thoroughly examined within the context of MV −chains,semi-simple MV −algebras and Hyperarchimedean structures. Furthermore, we provide characterizations for these ideals, offering equivalent definitions that enhance our understanding of their nature. Our investigation also encompasses the relationships between these special Z−ideals and other types of ideals, such as the minimal prime ideals and the maximal ideals. Overall, this paper aims to provide a comprehensive analysis of special Z−ideals in MV −algebras.

Triangle algebras are an important variety of residuated lattices enriched with two approximation‎ ‎operators as well as a third angular point (different from 0 and 1)‎. ‎They provide a well-defined mathematical framework for formalizing the use of closed intervals derived from a bounded lattice as truth values‎, ‎with a set of structured axioms‎. ‎This paper introduces the concept of relative co-annihilator of a subset within the framework of triangle algebras‎. ‎As filters of triangle algebras‎, ‎these relative co-annihilators are explored and some of their properties and characterizations are given‎. ‎A meaningful contribution of this work lies in its proof that the relative co-annihilator of a subset $T$ with respect to another subset $Y$ in a triangle algebra $\mathcal{L}$ inherits specific filter's characteristics of $Y$‎. ‎More precisely‎, ‎if $Y$ is a Boolean filter of the second kind‎, ‎then the co-annihilator of $T$ with respect to $Y$ is also a Boolean filter of the second kind‎. ‎The same statement applies when we replace the Boolean filter of the second kind with an implicative filter‎, ‎pseudo complementation filter‎, ‎Boolean filter‎, ‎prime filter‎, ‎prime filter of the third kind‎, ‎pseudo-prime filter‎, ‎or involution filter‎, ‎respectively‎. ‎Finally‎, ‎we establish some conditions under which the co-annihilator of $T$ relative to $Y$ is a prime filter of the second kind‎.

L-algebras, connected to algebraic logic and quantum structures, were first introduced by Rump [13]. In [5], the number of some finite L-algebras is counted. But classifying and finding examples of L-algebras is not always an easy task and is very important. So, in this paper, we classify the set of all non-isomorphic L-algebras up to order 4. For this, we define the notion of partial and total conditions and by using them, we characterize all of the L-algebras of orders 2, 3 and 4. We prove that that there are 5 L-algebras of order 3 and 44 L-algebras of order 4, up to isomorphism.

MTL-algebras, the algebraic counterparts of Monoidal t-norm logic are studied and Chinese Remainder Theorem for MTL-algebras is established. Semilocal MTL– algebras are introduced and briefly characterized.

Intermediate quantifiers are expressions of natural language, for example “most, almost all, many, a few” using which we quantify a number of some objects in a given universe. We have shown in [23] that all valid syllogisms with intermediate  quantifiers are a consequence of only two algebraic inequalities and one equality. The result was obtained in the formalism  of Lukasiewicz fuzzy type theory whose truth values form a linearly ordered complete MV-algebra. In this paper we will  prove that the same holds if we replace MV-algebra by a much more general IEQ-algebra (involutive EQ-algebra).

Two-generated free MV -algebras are described in the variety of Sωn -algebras

In this work, using some tools of Lie theory, we compute the Lie algebra of the Shearlet group regarding as a 3-fold semidirect product Lie group. As we will see, it is a 3-fold semidirect sum of Lie algebras.

We introduce the notions of $\mathcal{T}_{M}$-amenability and $\phi$-$\mathcal{T}_{M}$-amenability. Then, we characterize $\phi$-$\mathcal{T}_{M}$-amenability  in terms of $WAP$-diagonals and $\phi$-invariant means. Some concrete cases are also discussed.

The notion of a (branchwise) commutative BI-algebra is presented, and some related properties are investigated. We show that the class of commutative BH-algebras is broader than the class of commutative BI-algebras. Moreover, we prove every singular BI-algebra is a BH-algebra. Also, we define the commutative ideals in BI-algebras and characterize the commutative BI-algebras in terms of commutative ideals

We present an algorithm for computing A-annihilated elements of the form QI[1] in H*QS0 where I runs through admissible sequences of positive excess. This is algorithm with polynomial time complexity to address a sub-problem of an unsolved problem in algebraic topology known as the hit problem of Peterson which is likely to be NP-hard.

In this article, with the aim of further investigating BL-algebras, the concepts of Unity Co-annihilator-filters (UC-filters) is introduced and discussed. Also, for the faster study of UC-filters in BL-algebras, some equivalent conditions are obtained, and (with some examples) it is shown that these filters have differences. In addition, we consider several additional  conditions imposed on UC-filters and prime filters and establish links between them. So, we get relationships between  these types of filters and prime filters in BL-algebras. Finally, the form of all UC-saturated ∨-closed subsets of a G- algebras (by the concept of UC-saturated ∨-closed subsets) is stated.