We extend Nesterov’s semidefinite programming characterization of squared functional systems to cones of sum-of-squares elements in general abstract algebras. Using algebraic techniques such as isomorphism, linear isomorphism, tensor products, sums and direct sums, we show that many concrete cones are in fact sum-of-squares cones with respect to some algebra, and thus representable by the cone ...

Let V = B(H) or S(H), where B(H) is the algebra of bounded linear operator acting on the Hilbert space H, and S(H) is the set of self-adjoint operators in B(H). Denote the numerical range of A ∈ B(H) by W (A) = {(Ax, x) : x ∈ H, (x, x) = 1}. It is shown that a surjective map φ : V→ V satisfies W (AB +BA) =W (φ(A)φ(B) + φ(B)φ(A)) for all A,B ∈ V if and only if there is a unitary operator U ∈ B(H...

The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry, Computer Science, Topological Graph Theory and Metric Geometry. In this paper we propose the basic notions of such a theory and some applications: we replace the cl...

1. Modules: 4/2/13 1 2. Quotient Modules: 4/4/13 3 3. The Isomorphism Theorems: 4/9/13 5 4. Universal Properties: 4/11/13 7 5. The Tensor Product: 4/16/13 10 6. More Tensor Products: 4/18/13 12 7. Exact Sequences: 4/23/13 14 8. Projective and Injective Modules: 4/25/13 17 9. Finitely Generated Modules Over a Euclidean Domain: 4/30/13 19 10. Finitely Generated Modules Over a PID: 5/2/13 21 11. T...

Let ~ H and ~ K be finite composition series of a group G. The intersections Hi ∩ Kj of their members form a lattice CSL( ~ H, ~ K) under set inclusion. Improving the Jordan-Hölder theorem, G. Grätzer, J.B. Nation and the present authors have recently shown that ~ H and ~ K determine a unique permutation π such that, for all i, the i-th factor of ~ H is “down-and-up projective” to the π(i)-th f...

We propose a system for user-aided image localization in urban regions by exploiting the inherent graph like structure of urban streets, buildings and intersections. In this graph the nodes represent buildings, intersections and roads. The edges represent “logical links” such as two buildings being next to each other, or a building being on a road. We generate this graph automatically for large...

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...

In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...