相关论文: A Note on $g$-Angle between Two Subspaces in a Nor…
The sum theorem and its corollaries are proved for a countable family of zero-dimensional (in the sense of small and large inductive bidimensions) p-closed sets, using a new notion of relative normality whose topological correspondent is…
Double coset spaces of adelic points on linear algebraic groups arise in the study of global fields; e.g., concerning local-global principles and torsors. A different type of double coset space plays a role in the study of semi-global…
We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers defined in terms of Carleson measures.
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…
Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines…
The idea of convex sets and various related results in 2-Probabilistic normed spaces were established in [HR]. In this paper, We obtain the concepts of convex series closedness, convex series compactness, boundedness and their…
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
A "Two-Spaceship Paradox" in special relativity is resolved and discussed. We demonstrate a nonstandard resolution to the "two-spaceship paradox" by explicit calculation using Generalized Principle of limiting 4-dimensional symmetry…
In this paper we define a space $\ghu{M}$ of Hardy--Goldberg type on a measured metric space satisfying some mild conditions. We prove that the dual of $\ghu{M}$ may be identified with $\gbmo{M}$, a space of functions with "local" bounded…
We establish a two-weight fractional Poincar\'e-Sobolev sandwich, consisting of a two-weight fractional Poincar\'e-Sobolev inequality and a two-weight embedding from the first-order Sobolev space to a Triebel-Lizorkin space defined via a…
Let $\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive operator on $\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of operators in semi-Hilbertian space $\mathcal{B}_A(\mathcal{H})$ that generalize and…
Consider a complex Hilbert space $\left(\mathcal{H}, \langle \cdot, \cdot \rangle\right)$ equipped with a positive bounded linear operator $A$ on $\mathcal{H}$. This induces a semi-norm $\|\cdot\|_A$ through the semi-inner product $\langle…
Let $(G,u)$ be an archimedean norm-complete dimension group with order unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of $G$ which are closed with respect to the canonical norm of…
Recently a new approach to varying exponent $L^{p(\cdot)}$ space norms employing weak solutions to first order ordinary differential equations was initiated by the author. The duality of these ODE-determined $L^{p(\cdot)}$ spaces is…
Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying…
The lack of an inner product structure in Banach spaces yields the motivation to introduce a semi-inner product with a more general axiom system, one missing the requirement for symmetry, unlike the one determing a Hilbert space. We use it…
We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.
Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…
Every graph G can be embedded in a Euclidean space as a two-distance set. The Euclidean representation number of G is the smallest dimension in which G is representable by such an embedding. We consider spherical and J-spherical…