We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A∗ of A∗. The class of dual Banach algebras includes all W ∗-algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception...

let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

With every σ-ideal I on a Polish space we associate the σ-ideal generated by closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the...

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...

There are two notions of amenability for discrete equivalence relations. The \global" amenability (which is usually referred to just as \amenability") is the property of existence of leafwise invariant means, which, by a theorem of Connes{Feldman{Weiss, is equivalent to hyperrniteness, or, to being the orbit equivalence relation of a Z-action. The notion of \local" amenability applies to equiva...

Fuzzy ideal set and fuzzy local function of fuzzy ideals with fuzzy topologies were introduced and studied by D. Sarker [10]. The purpose of this paper deals with new sort of fuzzy ideal and fuzzy local function namely fuzzy ideal and r-fuzzy open local function. Many of its characterizations, properties and connections between it and other corresponding fuzzy notions are studied. Also, we intr...

We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

The relative densities of rational primes q, such that a given rational prime p is a square of either a principal or a non-principal ideal in the quadratic number field Q( √ pq), essentially depend on the residue classes of both p and q modulo 4. The computation of these densities is complete when at least one residue of p or q is not equal to 1 modulo 4. When both residues are equal to 1 modul...