Abbas Sahleh

University of Guilan · Department of Mathematics

In the present paper, we generalize the notion of convex contraction mappings to weak convex contraction mapping of order m (m ≥ 2), and prove that the class of weak convex contraction of order m is strong enough to generate a fixed point on a complete metric space with a w-distance but do not force the mapping to be continuous at the fixed point,...

In this paper, we will use the categorical approach to Hilbert \(C^{\ast}\)-modules over a commutative \(C^{\ast}\)-algebra to investigate the approximately orthogonality preserving mappings on Hilbert \(C^{\ast}\)-modules over a commutative \(C^{\ast}\)-algebra. Indeed, we show that if \(\Psi:\Gamma \rightarrow \Gamma^{\prime} \) is a nonzero \( C...

Introduction and preliminaries Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules. Let A be a C∗-algebra. An right inner product A-mod...

In this paper, we introduce the concept of trace-open projections in the second dual \( \mathcal {A}^{**} \), of a \( C^* \)-algebra \( \mathcal {A} \). This new concept is applied to show that if there is a faithful normal semi-finite trace \( \tau \) on \( \mathcal {A}^{**} \) such that \( 1_{ \mathcal {A}^{**} } \) is a \( \tau \)-open projectio...

Let X, Y and Z be Banach spaces and let f: X × Y → Z be a bounded bilinear map. In this paper we study the relation between Arens regularity of f and the reflexivity of Y. We also give some conditions under which the Arens regularity of a Banach algebra A implies the Arens regularity of certain Banach right module action of A.

In this article, weshow that module amenability with the canonical action of restricted semigroup algebra l1r (S) and semigroup algebra l1(Sr) are equivalent, where Sr is the restricted semigroup of associated to the inverse semigroup S. We use this to give a characterization of module amenability of restricted semigroup algebra l1r (S) with the ca...

We study Arens regularity of the left and right module actions of on , where is the nth dual space of a Banach algebra , and then investigate (quotient) Arens regularity of as a module extension of Banach algebras.

Let 𝒜 be a Banach algebra and 𝒜 its second dual equipped with the first Arens product. We consider three 𝒜-bimodule structures on the fourth dual of 𝒜. This paper discusses the situation that makes these structures coincide.

In this paper we investigate n-approximately weak amenability of a Banach algebra A, and show that for n ≥ 2, n-approximately weak amenability passes from A" to A, where A" is the second dual of A equipped with the first Arens product. Also we prove that under certain condition n-approximately weak amenability inherits by closed subalgebras of A.

Let A* be dual of a locally convex algebra A, with dual topology and φ ** ** be the natural map of A into A (Here A denotes the bidual of A with weak* topology.) In this paper, we prove that π(A) is a right ideal of A** with respect to the first Arens product if and only if A is a left weak Banach precompact. Also we obtain some related results.

We consider the enveloping semigroup of a flow generated by the action of a semitopological semigroup on any of its semigroup compactifications and explore the possibility of its being one of the known semigroup compactifications again. In this way, we introduce the notion of E-algebra, and show that this notion is closely related to the reductivit...