arXiv subjects
Publications and source records attributed to Ali Rejali.
Let $ ( X , d ) $ be a metric space and $ A $ be a commutative Banach algebra such that $ Δ( A ) $ be nonempty. In this paper, we provide necessary and sufficient conditions, under which $ C_{BSE} ( Δ(A) ) $ is a Dual Banach algebra. Moreover, we provide some conditions for that $ Lip_α ( X , A ) $ is a Dual Banach algebra.
Takahasi and Hatori introduced a class of commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein-type inequality. Baised on their results we introduced a class of commutative Fréchet algebras which satisfy this property. We show that Fréchet C*-algebras and uniform Fréchet algebras are BSE-algebras.
A class of commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein-type inequality was introduced by Takahasi and Hatori. We generalize this property for the commutative Frechet algebra A. Furthermore, some of the main results in the class of Banach algebras, will be verified and generalized for the Frechet case.
Let A and B be two commutative semisimple Frechet algebras. We first give a characterization of the multiplier algebra of the direct sum of A and B. We then prove that A \oplus B is a BSE-algebra if and only if A and B are BSE-algebras. Furthermore, for a closed ideal I of A, we study multipliers of ideals and quotient algebras of A and show that I and A/I are BSE-algebras, under certain conditions.
Amenability modulo an ideal of a Banach algebra have been defined and studied. In this paper we introduce the concept of amenability modulo an ideal of a Frechet algebra and investigate some known results about amenability modulo an ideal of a Frechet algebra. Also we show that a Frechet algebra A is amenable modulo an ideal if and only if A is isomorphic to a reduced limit of amenable modulo an ideal of Banach algebras.
For a Banach algebra A and a closed ideal I, the notion of bounded approximate diagonal modulo I has been studied and investigated. In this paper we define the notion of locally bounded approximate diagonal modulo an ideal I for a Frechet algebra A and obtain the relation between amenability modulo an ideal I and the existence of locally bounded approximate diagonals modulo I.
We provide a survey of the similarities and differences between Banach and Frechet algebras including some known results and examples. We also collect some important generalizations in abstract harmonic analysis; for example, the generalization of the concepts of vector-valued Lipschitz algebras, abstract Segal algebras, Arens regularity, amenability, weak amenability, ideal amenability, etc.
The concept of configuration was first introduced to give a characterization for the amenability of groups. Then the concept of two-sided configuration was suggested to provide normality to study the group structures more efficiently. It has been interesting that for which groups, two-sided configuration equivalence would imply isomorphism. We introduce a class of groups, containing polycyclic and FC groups, which for them, the notions of two-sided configuration equivalence and isomorphism coincide.
The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we investigate some condition on configuration pairs, which leads to isomorphism. We introduce a somewhat different notion of configuration equivalence, namely strong configuration equivalence, and prove that strong configuration equivalence coincides with isomorphism.
Giving a condition for the the amenability of groups, Rosenblatt and Willis, first introduced the concept of configuration. From the beginning of the theory, the question whether the concept of configuration equivalence coincides with the concept of group isomorphism was posed. We negatively answer this open question by introducing two non-isomorphic, solvable and hence amenable groups which are configuration equivalent. Also, we will study some types of subgroups in configuration equivalent groups. In particular, we will prove this conjecture, due to Rosenblatt and Willis, that configuration equivalent groups, both include the free non-Abelian group of same rank or not. Finally, we prove that two-sided equivalent groups have same class numbers.
For weighted group convoltion measure algebra we construct a representation on reflexsive space.
In this paper we investigate the compact and weakly compact multipliers of the Herz-algebras $A_p(G)$. Let $B_p(G)$ be the space of pointwise multipliers of $A_p(G)$. We show that there is a topological invariant mean on $B^*_p (G)$. Furthermore, we show that if $B^*_p(G)$ is separable, then $G$ is a discrete group.
Let $G$ be a locally compact group, $A_p (G)$ be the Herz algebra of $G$ associated with $1 <p< \infty$. We show that $A_p (G)$ is Arens regular if and only if $G$ is a discrete group and for each countable subgroup $H$ of $G$, $A_p (H)$ is Arens regular. In the case $G$ is a countable discrete group we investigate the relations between Arens regularity of $A_p (G)$ and the iterated limit condition. We consider the problem of Arens regularity of $l^1 (G)$ as a subspace of $A_p (G)$. A few related results when the unit ball of $(l^1 (G),.,A_p(G))$ is bounded under $\|.\|_1$-norm are also determined.
In this paper we prove that the limiting distribution of the Chromatic number of a random graph $\mathcal{G}_{n,p}$, with fixed edge-probability $p$, after appropriate centering and scaling is Normal, when the number of vertices $n$, goes to infinity.
We show that every Banach algebra A admits a representation on a certain Banach space E. In particular, any Banach algebra A contained in autoperiodic functionals on A such that separate the points of A could be imbedded in B(E) for some reflexive Banach space E.
Let WAP(A) be the space of all weakly almost periodic functionals on a Banach algebra A. The Banach algebra A for which the natural embedding of A into WAP(A)* is bounded below is called a WAP-algebra. We show that the second dual of a Banach algebra A is a WAP-algebra, under each Arens products, if and only if A** is a dual Banach algebra. This is equivalent to the Arens regularity of A. For a locally compact foundation semigroup S, we show that the absolutely continuous semigroup measure algebra M_a(S) is a WAP-algebra if and only if the measure algebra M_b(S) is so.
In 2005, Abdollahi and Rejali, studied the relations between paradoxical decompositions and configurations for semigroups. In the present paper, we introduce another concept of amenability on semigroups and groups which includes amenability of semigroups and inner-amenability of groups. We have the previous known results to semigroups and groups satisfying this concept.