Let A and B be Banach algebras with bounded approximate identities let Φ:A→B a surjective continuous linear map which preserves two-sided zero products (i.e., Φ(a)Φ(b)=Φ(b)Φ(a)=0 whenever ab=ba=0). We show that Φ is weighted Jordan homomorphism provided product determined weakly amenable. These conditions are in particular fulfilled when the group algebra L1(G) G any locally compact group. also...

The motivation for this paper is three-fold. First, we study the connectivity properties of the homomorphism order of directed graphs, and more generally for relational structures. As opposed to the homomorphism order of undirected graphs (which has no non-trivial finite maximal antichains), the order of directed graphs has finite maximal This research was partially supported by the EU Research...

We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation definable (1) by linear tree (2) homomorphism. present algorithms construct equivalent such transducers if they exist.

A near-representation of a group G is a map M : G → GL(V ), where V is a complex linear space and Mgh ≈MgMh for all g, h ∈ G, i.e. M is approximately a homomorphism. Analogously to the representation theory of finite groups, we investigate the properties of nearrepresentations and show that they are equivalent to unitary nearrepresentations, and can be split to stably irreducible constituents. ...

in this paper we will prove that the simple group g2(q) where 2 < q = 1(mod3)is recognizable by the set of its order components, also other word we prove that if g is anite group with oc(g) = oc(g2(q)), then g is isomorphic to g2(q).

In this paper we survey results related to homomorphism dualities for graphs, and more generally, for finite structures. This is related to some of the classical combinatorial problems, such as colorings of graphs and hypergraphs, and also to recently intensively studied Constraint Satisfaction Problems. On the other side dualities are related to the descriptive complexity and First Order defin...

We consider a database composed of a set of conceptual graphs. Using conceptual graphs and graph homomorphism it is possible to build a basic query-answering mechanism based on semantic search. Graph homomorphism defines a partial order over conceptual graphs. Since graph homomorphism checking is an NP-Complete problem, the main requirement for database organizing and managing algorithms is to ...

We consider mappings between edge sets of graphs that lift tensions to tensions. Such mappings are called tension-continuous mappings (shortly mappings). Existence of a mapping induces a (quasi)order on the class of graphs, which seems to be an essential extension of the homomorphism order (studied extensively, see [10]). In this paper we study the relationship of the homomorphism and orders. W...