Uniformly convex space information

mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity was...

strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space is...

the Lp-spaces are uniformly smooth (and uniformly convex). Enflo proved that the class of Banach spaces that admit an equivalent uniformly convex norm coincides...

( t ) . {\displaystyle n(t).} Uniformly convex spaces are super-reflexive. Let X {\displaystyle X} be uniformly convex, with modulus of convexity δ X...

locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They...

r} is compact. The function f has a unique global minimum on Rn. A uniformly convex function, with modulus ϕ {\displaystyle \phi } , is a function f {\displaystyle...

locally convex. Banach spaces, Hilbert spaces and Sobolev spaces are other well-known examples of TVSs. Many topological vector spaces are spaces of functions...

geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral...

subset of Y . {\displaystyle Y.} Uniformly continuous extensions Suppose that f : D → Y {\displaystyle f:D\to Y} is a uniformly continuous map from a dense...

Fréchet space – A locally convex topological vector space that is also a complete metric space Hardy space – Concept within complex analysis Hilbert space –...

compact. The uniformly continuous image of a precompact set is precompact. Although the notion of total boundedness is closely tied to metric spaces, the greater...

Under relatively general conditions (the space is a possibly infinite-dimensional uniformly convex space, there can be infinitely many sites of a general...

"how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity...

member of a uniformly equicontinuous set of functions is uniformly continuous, and every finite set of uniformly continuous functions is uniformly equicontinuous...

N is any complete metric space and f is any uniformly continuous function from M to N, then there exists a unique uniformly continuous function f′ from...

of uniform embeddability among Banach spaces, and the distortion was an auxiliary device in his proof." A uniformly convex space is a Banach space so...

of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star...

Hilbert space is a uniformly convex Banach space. This subsection employs the Hilbert projection theorem. If C is a non-empty closed convex subset of...

cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular)...

corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices...

is either a compact, or a convex subset of a normed space. However, a uniformly continuous function on a general metric space admits a concave modulus...

locally convex space. A family B {\displaystyle {\mathcal {B}}} of subsets of a topological vector space Y {\displaystyle Y} is said to be uniformly bounded...