In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

Ting, S.-T. and S.-Y. Zhao, The general Steiner problem in Boolean space and application, Discrete Mathematics 90 (1991) 75-84. The Steiner problem is to find the minimum point P of sum of distances C;=‘=,p=@(P)whereP,i=l,..., n, are given points in Euclidean plane. It is solved for n = 3, [l]. When n > 3 even approximation is unsatisfactory [3]. In Boolean space the distance of Boolean points ...

In this paper, we prove the following form of Stone’s representation theorem: Let ∑ be a σ -algebra of subsets of a set X . Then there exists a totally disconnected compact Hausdorff space K for which ( ∑ ,∪,∩) and (C(K),∪,∩) , where C(K) denotes the set of all clopen subsets of K , are isomorphic as Boolean algebras. Furthermore, by defining appropriate joins and meets of countable families in...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

There are three important steps in the proof the BDF theorem for essentially normal operators having essential spectrum X ⊆ C. (1) Ext(X) has a neutral element. (2) Ext(X) is a group (i.e., has inverses). (3) Ext(X) depends only on the homotopy class of X. In this lecture we will exhibit the neutral element of Ext(X) and describe the generalization of that result to noncommutative C∗-algebras (...

We prove two results on the stability spectrum for Lω1,ω . Here S m i (M) denotes an appropriate notion (at or mod) of Stone space of m-types over M . Theorem A. Suppose that for some positive integer m and for every α < δ(T ), there is an M ∈ K with |S i (M)| > |M |iα(|T |). Then for every λ ≥ |T |, there is an M with |S i (M)| > |M |. Theorem B. Suppose that for every α < δ(T ), there is Mα ∈...