Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors [9]. We show that several parameters on forests can be realized as forest algebra homomorphisms from the free forest algebra into algebras which retain the equational axioms of forest algebras. This includes the number of nodes, the n...

In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra T of a distance-regular graph that has q-Racah type; (ii) the q-tetrahedron algebra ⊠q which is a q-deformation of the three-point sl2 loop algebra. Assuming that every irreducible T -module is thin, we display an algebra homomorphism from ⊠q into T and show that T is generated by the imag...

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...

Let E be a row-finite directed graph. We prove that there exists a C∗algebra C∗ min (E) with the following co-universal property: given any C∗-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections are nonzero, there is a canonical homomorphism from B onto C∗ min (E). We also identify when a homomorphism from B to C∗ min (E) obtained from the co-universal p...

Although every computable data type has an initial algebra speci-cation with hidden functions, it may happen that some of the homo-morphic images of the data type are not models of the speciication. The latter are reducts of algebras that would be models of the specii-cation if all its functions were visible, whereas the homomorphic images of the data type are independent of the speciication an...

We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra (or of a derivation from A into a Ban...

An algebra homomorphism ψ from the q-deformed algebra U q (iso 2) with generating elements I, T 1 , T 2 and defining relations [I, T 2 ] q = T 1 , [T 1 , I] q = T 2 , [T 2 , T 1 ] q = 0 (where [A, B] q = q 1/2 AB − q −1/2 BA) to the extensionˆU q (m 2) of the Hopf algebra U q (m 2) is constructed. The algebra U q (iso 2) at q = 1 leads to the Lie algebra iso 2 ∼ m 2 of the group ISO(2) of motio...

1. Introduction Let B be a commutative Banach algebra, and let 6 be a homomorphism from B into a Banach algebra A. In this paper we are concerned with establishing conditions on A and B which ensure that 6 is continuous. If A is semisimple, it is well known that any such homomorphism must be continuous, and therefore we shall be interested in cases where A is not semisimple. Questions of this n...