The generalized Day norm. Part I. Properties
Journal Title: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica - Year 2017, Vol 71, Issue 2
Abstract
In this paper we introduce a modification of the Day norm in c0(Γ) and investigate properties of this norm.
Authors and Affiliations
Monika Budzynska, Aleksandra Grzesik, Mariola Kot
A survey of a selection of methods for determination of Koebe sets
In this article we take over methods for determination of Koebe set based on extremal sets for a given class of functions.
Entire functions of exponential type not vanishing in the half-plane Iz>k, where k>0
Let P(z) be a polynomial of degree n having no zeros in |z|<k, k≤1, and let Q(z):=znP(1/z). It was shown by Govil that if max|z|=1|P′(z)| and max|z|=1|Q′(z)| are attained at the same point of the unit circle |z|=1, then...
Generalized trend constants of Lipschitz mappings
In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point...
On branchwise commutative pseudo-BCH algebras
Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is p...
The generalized Day norm. Part II. Applications
In this paper we prove that for each 1<p,p~<∞, the Banach space (lp~,∥⋅∥p~) can be equivalently renormed in such a way that the Banach space (lp~,∥⋅∥L,α,β,p,p~) is LUR and has a diametrically complete set with empty int...