Search results for "Unit sphere"
showing 10 items of 54 documents
A Short Proof that Some Mappings of the Unit Ball of ℓ2 Are Never Nonexpansive
2020
It is known that some particular self-mappings of the closed unit ball Bl2 of l2 with no fixed points cannot be nonexpansive with respect to any renorming of l2. We give here a short proof of this ...
On Pietsch measures for summing operators and dominated polynomials
2012
We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.
Kadec and Krein–Milman properties
2000
Abstract The main goal of this paper is to prove that any Banach space X with the Krein–Milman property such that the weak and the norm topology coincide on its unit sphere admits an equivalent norm that is locally uniformly rotund.
Hamel-isomorphic images of the unit ball
2010
In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Unit Operations in Approximation Spaces
2010
Unit operations are some special functions on sets. The concept of the unit operation originates from researches of U. Wybraniec-Skardowska. The paper is concerned with the general properties of such functions. The isomorphism between binary relations and unit operations is proved. Algebraic structures of families of unit operations corresponding to certain classes of binary relations are considered. Unit operations are useful in Pawlak's Rough Set Theory. It is shown that unit operations are upper approximations in approximation space. We prove, that in the approximation space (U, R) generated by a reflexive relation R the corresponding unit operation is the least definable approximation i…
Homeomorphisms of finite distortion: discrete length of radial images
2008
AbstractWe study homeomorphisms of finite exponentially integrable distortion of the unit ball Bn onto a domain Ω of finite volume. We show that under such a mapping the images of almost all radii (in terms of a gauge dimension) have finite discrete length. We also show that our dimension estimate is essentially sharp.
Rescaling principle for isolated essential singularities of quasiregular mappings
2012
We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.
Conformal Metrics on the Unit Ball in Euclidean Space
1998
On quasi-denting points, denting faces and the geometry of the unit ball ofd(w, 1)
1994
Ultrarelativistic bound states in the spherical well
2016
We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator $(-\Delta )^{1/2}$, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral datafor lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled $E_{(k,l)}$ series. For each orbital label $l=0,1,2,...$ the label $k =1,2,...$ enumerates consecutive $l$-th series eigenvalues. Each of them is $2l+1$-degenerate. …