in this paper, we introduce the notion of multiplier in -algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and ( -derivations in -algebras. we introduce the concept of idempotent multipliers in bl-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. also, we introduce...

intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...

The well-known Lawvere category [0,∞] of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But [0,∞] has another such structure, given by multiplication, which is *-autonomous and a CL-algebra (linked with classical linear logic). Normed sets, with a norm in [0,∞], inherit thus two symmetric monoidal closed structures, and categories enri...

This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system paramete...

Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in ...

In this two-part paper, a common algebraic framework is introduced for the frozen-time analysis of stability and H"-optimization in slowly time-varying systems, based on the notion of a normed algebra on which local and global products are defined. Relations between local stability, local (near) optimality, lotal coprime factorization, and global versions of these properties are sought. The fra...

Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in ...

In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains,...

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

Let ‖.‖ be a norm on the algebra Mn of all n × n matrices over C. An interesting problem in matrix theory is that ”are there two norms ‖.‖1 and ‖.‖2 on Cn such that ‖A‖ = max{‖Ax‖2 : ‖x‖1 = 1} for all A ∈ Mn. We will investigate this problem and its various aspects and will discuss under which conditions ‖.‖1 = ‖.‖2. 1 Preliminaries Throughout the paper Mn denotes the complex algebra of all n× ...