相关论文: A formula for the $g$-angle between two subspaces …
Around 1930, K. Menger expressed his interest in the concept of abstract angle function. He introduced a general definition of this notion for metric and semi-metric spaces. He also proposed two problems concerning conformal embeddability…
Let $\mathcal S=\{s_1<s_2<s_3<\ldots\}$ be the sequence of all natural numbers which can be represented as a sum of two squares of integers. For $X\ge2$ we denote by $g(X)$ the largest gap between consecutive elements of $\mathcal S$ that…
In this paper we estimate the norm of operator acting from one Bilateral Grand Lebesgue Space (BGLS) into other Bilateral Grand Lebesgue Space. We also give some examples to show the sharpness of offered inequalities.
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
We study the distribution of the angles between Oseledets subspaces and their log-integrability, focusing on dimension $2$. For random i.i.d. products of matrices, we construct examples of probability measures on $\mathrm{GL}_2(\mathbb{R})$…
We give an expression for the norm of the space constructed by Tsirelson. The implicit equation satisfied by this norm is dual to the implicit equation for the norm of the dual of Tsirelson space given by Figiel and Johnson. The expression…
In this paper, we investigate the general form of surjective (not necessarily linear) isometries T : A-> B between subspaces A and B of C(X;E) and C(Y;F), respectively.
A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
In this paper, we improve the moment estimates for the gaps between numbers that can be represented as a sum of two squares of integers. We consider certain sum of Bessel functions and prove the upper bound for its weighted mean value. This…
Let $\Delta$ be a $d$-dimensional normal pseudomanifold, $d \ge 3.$ A relative lower bound for the number of edges in $\Delta$ is that $g_2$ of $\Delta$ is at least $g_2$ of the link of any vertex. When this inequality is sharp $\Delta$ has…
Problems of absolute G measurements, its temporal and range variations from both experimental and theoretical points of view are discussed, and a new universal space project for measuring G, G(r) and G-dot promising an improvement of our…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
A notion of orthogonality in multisymplectic geometry has been developed by Cantrijn, Ibort and de Le\'on and used by many authors. In this paper, we review this concept and propose a new type of orthogonality in multisymplectic geometry;…
For a Banach space $X$ we shall denote the set of all closed subspaces of $X$ by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$ with a topology. The main purpose of the present paper is to survey results on two…
We derive a formula which is a lower bound on the dimension of trivariate splines on a tetrahedral partition which are continuously differentiable of order $r$ in large enough degree. While this formula may fail to be a lower bound on the…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called…
In the present paper, we introduce the notion of $E$-$g$-frames for a separable Hilbert spaces $\mathcal H$, where $E$ is an invertible infinite matrix mapping on the Hilbert space $\mathop\oplus\limits_{n=1}^{\infty}\mathcal H_n$. We study…
We describe the T-space of central polynomials for both the unitary and the nonunitary finite dimensional Grassmann algebra over a field of characteristic p not equal to 2 (infinite field in the case of the unitary algebra).