A two-sided sequence (cn)n∈Z with values in a complex unital Banach algebra is a cosine sequence if it satisfies cn+m + cn−m = 2cncm for any n,m ∈ Z with c0 equal to the unity of the algebra. A cosine sequence (cn)n∈Z is bounded if supn∈Z ‖cn‖ < ∞. A (bounded) group decomposition for a cosine sequence c = (cn)n∈Z is a representation of c as cn = (b n +b−n)/2 for every n ∈ Z, where b is an inver...

Let V be a non empty additive loop structure and let V1 be a subset of V . We say that V1 has inverse if and only if: (Def. 1) For every element v of V such that v ∈ V1 holds −v ∈ V1. Let V be a non empty additive loop structure and let V1 be a subset of V . We say that V1 is additively-closed if and only if: (Def. 2) V1 is add closed and has inverse. Let V be a non empty additive loop structur...

This thesis examines the performance improvements that can be made by exploiting parallel processing in symbolic mathematical computation. The study focuses on the use of high-level parallelism in the case where the number of processors is fixed and independent of the problem size, as in existing multiprocessors. Since seemingly small changes to the inputs can cause dramatic changes in the exec...

We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class K of algebraic systems. One characterization of this concept states that A is locally embedded in K iff it is a subsystem of an ultraproduct of systems from K....

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X)). An operator S ∈ B(X) is a generalised inverse of T if TST = T . In this paper we look at the Jörgens algebra, an algebra of operators on a dual system, and characterise when an operator in that algebra has a generalised inverse that is also in the algebra. This result is then applied to bounded inner product...

let $a$ be a nite dimensional $k-$algebra and $r$ be a locally bounded category such that $r rightarrow r/g = a$ is a galois covering de ned by the action of a torsion-free group of automorphisms of $r$. following [30], we provide criteria on the convex subcategories of a strongly simply connected category r in order to be a cycle- nite category and describe the module category of $a$. we pro...

let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ M r(x) for all x ∈ E, where r( · ) denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple C∗-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.