Equicontinuous schauder bases and compatible locally convex topologies
نویسندگان
چکیده
منابع مشابه
Locally Quasi-Convex Compatible Topologies on a Topological Group
For a locally quasi-convex topological abelian group (G, τ), we study the poset C (G, τ) of all locally quasi-convex topologies on G that are compatible with τ (i.e., have the same dual as (G, τ)) ordered by inclusion. Obviously, this poset has always a bottom element, namely the weak topology σ(G, Ĝ). Whether it has also a top element is an open question. We study both quantitative aspects of ...
متن کاملLocally Equicontinuous Dynamical Systems
A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in l∞(Z) form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, w...
متن کاملFractal Functions and Schauder Bases
1. Introduction. In recent years more and more attention has been paid in mathematical papers to fractal functions and to fractal sets. There are various definitions of those objects. We assume that a compact set K ∈ R d+1 is fractal, by definition, if its box (entropy) dimension dim b (K) = j for j = 0, 1,. .. , d + 1 and 0 < dim b (K) < d + 1. At the same time the function f : I d → R d , I =...
متن کاملSchauder bases under uniform renormings
Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. Mathematics Subject Classification (2000). 46B03.
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: Indagationes Mathematicae (Proceedings)
سال: 1974
ISSN: 1385-7258
DOI: 10.1016/1385-7258(74)90044-4