相关论文: Angles and Polar Coordinates In Real Normed Spaces
The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces by suitable intersections of balls. A subset $S$ of a normed…
This article is about the (minimal) sector containing the numerical range of the principal part of a linear second-order elliptic differential operator defined by a form on closed subspaces V of the first-order Sobolev space…
Using the notion of the normalized duality map it is characterized the class of the uniformly convex uniformly smooth Banach spaces in which each convex cone has a convex polar.
Associated to Birkhoff orthogonality, we study Birkhoff angles in a normed space and present some of their basic properties. We also discuss how to decide whether an angle is more acute or more obtuse than another. In addition, given two…
Polar spaces over finite fields are fundamental in combinatorial geometry. The concept of polar space was firstly introduced by F. Veldkamp who gave a system of 10 axioms in the spirit of Universal Algebra. Later the axioms were simplified…
A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…
We introduce the point degree spectrum of a represented space as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The notion of point degree spectrum…
We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of…
We introduce extensions of $\Delta$-points and Daugavet points in which slices are replaced by relative weakly open subsets (super $\Delta$-points and super Daugavet points) or by convex combinations of slices (ccs $\Delta$-points and ccs…
This paper is concerned with a new approach to coorbit space theory. Usually, coorbit spaces are defined by collecting all distributions for which the voice transform associated with a square-integrable group representation possesses a…
In this paper, we present a proof of Schauder estimate on Euclidean space and use it to generalize Donaldson's Schauder estimate on space with conical singularities in the following two directions. The first is that we allow the total cone…
The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a much simpler form. In this paper we provide simple…
The Erd\H{o}s-Anning theorem states that every point set in the Euclidean plane with integer distances must be either collinear or finite. More strongly, for any (non-degenerate) triangle of diameter~$\delta$, at most $O(\delta^2)$ points…
Based on the two decades old celebrated Paulsen problem and its solutions for Hilbert spaces by Kwok, Lau, Lee, Ramachandran, Hamilton, and Moitra, we formulate Paulsen problem for Banach spaces. We also formulate projection problem for…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators $\Gamma$ on a Hilbert space. Our assumption on $\Gamma$ is expressed in terms of…
Geometric quantiles are location parameters which extend classical univariate quantiles to normed spaces (possibly infinite-dimensional) and which include the geometric median as a special case. The infinite-dimensional setting is highly…
A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in $\mathbb{R}^n$ was studied extensively for the last 70 years. In this paper, we…
The inscribed angle theorem, a famous result about the angle subtended by a chord within a circle, is well known and commonly taught in school curricula. In this paper, we present a generalisation of this result (and other related circle…
In terms of triples of Banach spaces, we define a large class of boundary problems for ordinary differential equations (of arbitrary order) with singular coefficients.