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Let G be a locally compact topological group and X a compact space with continuous G-action. The main result of this essay states that the following statements are equivalent : 1) The action of G on X is topologically amenable ; 2) Every…

The main purpose of this paper is to unify the theory of actions of Hopf algebras, weak Hopf algebras and multiplier Hopf algebras to one of actions of weak multiplier Hopf algebras introduced by A. Van Daele and S. H. Wang. Using such…

In this paper, two related types of dualities are investigated. The first is the duality between left-invertible operators and the second is the duality between Banach spaces of vector-valued analytic functions. We will examine a pair…

We study Banach representability for actions of topological groups on groups by automorphisms (in particular, actions of groups on itself by conjugations). Every such action is Banach representable on some Banach space. The natural question…

This paper introduces and investigates novel properties of uaw-Dunford-Pettis operators on Banach spaces, exploring their relationships with other classes of operators. We further define and characterize new property of Banach lattices.…

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…

Let G be either a finite cyclic group of prime order or S^1. We find new relations between cohomology of a manifold (or a Poincare duality space) M with a G-action on it and cohomology of the fixed point set, M^G. Our main tool is the…

In this article, we introduce the notion of $p$-$(DPL)$ sets.\ Also, a factorization result for differentiable mappings through Dunford-Pettis $p$-convergent operators is investigated.\ Namely, if $ X ,Y $ are real Banach spaces and $U$ is…

In this article we shall focus on the derivations on module extension of Banach algebras and determine the general structure of them. Then we obtain some results concerning the automatic continuity of these mappings.

In representation theory, the double centraliser property is an important property for a module (bimodule). It plays a fundamental role in many theories. In this paper, we extend this property to complexes in derived categories of finite…

We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations.

Let $H$ be a compact subgroup of a locally compact group $G$ and let $m$ be the normalized $G$-invariant measure on homogeneous space $G/H$ associated with Weil's formula. Let $\varphi$ be a Young function satisfying $\Delta_2$-condition.…

We investigate weak amenability of the Banach algebra A(X) of approximable operators on a Banach space X and its relation to factorization properties of operators in A(X). We show that if A(X) is weakly amenable, then either A(X) is…

Weighted EP Banach space operators and Banach algebra elements are characterized using different kinds of factorizations. The results presented extend well-known characterizations of (weighted) EP matrices, (weighted) EP Hilbert space…

We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…

Assume that two algebraic varieties of finite type over the complex numbers are related by a morphism whose fibers are precisely the orbits for the action of a unipotent group. We show that the two varieties have the same topological Euler…

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

We discuss three problems related to connections on bimodules. These are left and right Leibniz rule for connections, left and right linearity of their curvatures and extension of connections to tensor products of modules.

We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking…

The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for…