Related papers: Angles and Polar Coordinates In Real Normed Spaces

A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic…

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, e.g., as lengths of catheti of right-angled triangles (defined via so-called quasi-orthogonality). These…

In this paper, we define probabilistic n-Banach spaces along with some concepts in this field and study convergence in these spaces by some lemmas and theorem.

Let $E$ be a $(\mathrm{IV})$-polyhedral Banach space. We show that, for each $\epsilon>0$, $E$ admits an $\epsilon$-equivalent $\mathrm{(V)}$-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its…

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists…

In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any…

Consider the polynomial ring in any finite number of variables over the complex numbers, endowed with the $\ell_1$-norm on the system of coefficients. Its completion is the Banach algebra of power series that converge absolutely on the…

In this article, concepts of well- and ill-posedness for linear operators in Hilbert and Banach spaces are discussed. While these concepts are well understood in Hilbert spaces, this is not the case in Banach spaces, as there are several…

Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan…

In a work by Artstein-Avidan and Milman the concept of polarity is generalized from the class of convex bodies to the larger class of convex functions. While the only self-polar convex body is the Euclidean ball, it turns out that there are…

In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric characterizations of these and related spaces. The results have…

We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show…

In this paper we study the regularity of embeddings of finite--dimensional subsets of Banach spaces into Euclidean spaces. In 1999, Hunt and Kaloshin [Nonlinearity 12 1263-1275] introduced the thickness exponent and proved an embedding…

We study Hilbert generated versions of nonseparable Banach spaces $\mathcal X$ considered by Shelah, Stepr\=ans and Wark where the behavior of the norm on nonseparable subsets is so irregular that it does not allow any linear bounded…

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

The standard Bloch sphere representation was recently generalized to the 'extended Bloch representation' describing not only systems of arbitrary dimension, but also their measurements. This model solves the measurement problem and is based…

We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the…

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

This article is a continuation of a paper of the first author \cite{F} about complex structures on real Banach spaces. We define a notion of even infinite dimensional real Banach space, and prove that there exist even spaces, including HI…

Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed…