Ordered Banach algebras and multi-norms: some open problems
نویسندگان
چکیده
منابع مشابه
An Example on Ordered Banach Algebras
Let B be a complex unital Banach algebra. We consider the Banach algebra A = B × C ordered by the algebra cone K = {(a, ξ) ∈ A : ‖a‖ ≤ ξ}, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in B. 1. Ordered Banach algebras The aim of this paper is to stress the aspect of the applicability of the ordered Banach algebra...
متن کاملIdeal Amenability of Banach Algebras and Some Hereditary Properties
Let A be a Banach algebra. A is called ideally amenable if for every closed ideal I of A, the first cohomology group of A with coefficients in I* is trivial. We investigate the closed ideals I for which H1 (A,I* )={0}, whenever A is weakly amenable or a biflat Banach algebra. Also we give some hereditary properties of ideal amenability.
متن کاملOrdered Variational Inequalities and Ordered Complementarity Problems in Banach Lattices
and Applied Analysis 3 Lemma 3. Let (X; ≽) be a Banach lattice. Then the positive coneX is weakly closed. Proof. It is clear that the positive coneX of the Banach lattice X is convex. We have mentioned that the positive coneX of the Banach latticeX is norm closed. ApplyingMazur’s lemma (see [12] or [15]), we have in a Banach space, a convex set is norm closed if and only if it is weakly closed....
متن کاملOn some open problems in cone metric space over Banach algebra
In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...
متن کاملSolutions to Some Open Problems on Totally Ordered Monoids
In this paper solutions to three open problems on ordered commutative monoids posed in [4] are presented. By an ordered monoid we always mean a totally ordered monoid. All the problems are related to the class of ordered commutative monoids which are homomorphic images of ordered free commutative monoids.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Positivity
سال: 2017
ISSN: 1385-1292,1572-9281
DOI: 10.1007/s11117-017-0488-7