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...

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.

Arabic character recognition of handwriting is addressed. A novel approach for the Arabic Character Recognition is presented based on statistical analysis of a typical Arabic text is presented. Results showed that the sub-word in Arabic language is the basic pictorial block rather than the word. The method of approximate stroke sequence is applied for the recognition of some Arabic characters i...

In this paper, we consider ultrapowers of Banach algebras as and the product $${{\bigcirc }_{{(J,\mathcal{U})}}}$$ on second dual algebras. For a algebra A, show that if there is continuous derivation from A into itself, then (A**, ) it. Moreover, X**, where X A-bimodule, ultrapower X; i.e., $${{(X)}_{\mathcal{U}}}$$ . Ultra (character) amenability investigated it will be shown every inner, ult...

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.

In recent years, there has been a flurry of activity relating notions linked to amenability or groups on one side, and combinatorial conditions linked to Ramsey theory on the other side. In this paper, we extend a result of Moore ([M2, theorem 7.1]) on the amenability of closed subgroups of S∞ to general Polish groups. A topological group is said to be amenable if every continuous action of the...

This paper aims to show that the amenability of K1 ×K2 is equivalent to the following condition: “If φ is a continuous positive definite function defined on K1 ×K2 and φ ≥ 0 then the constant function 1K1×K2 belongs to the spectrum of φ”, which K1 and K2 are locally compact hypergroups as defined by R. Jewett [1], with convolutions ∗1, ∗2 respectively.Our study deals with the cases of exponenti...

We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if G has property A relative to a family of subgroups H and if each H ∈ H has property A, then G has property A. This result leads to new classes of groups that hav...