Homotopy of projections and factorization in the unitary group of certain C*-algebras.
Hopf algebras of smooth functions on compact Lie groups
A -Hopf algebra is a -algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those -Hopf algebras which are given by the algebra of smooth functions on some compact Lie group , thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.
Hopf Extension Theorem of Measure
The authors have presented some articles about Lebesgue type integration theory. In our previous articles [12, 13, 26], we assumed that some σ-additive measure existed and that a function was measurable on that measure. However the existence of such a measure is not trivial. In general, because the construction of a finite additive measure is comparatively easy, to induce a σ-additive measure a finite additive measure is used. This is known as an E. Hopf's extension theorem of measure [15].
Horizontal lift of tensor fields of type (1,1) from a manifold to its tangent bundle of higher order
How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?
For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur...
How far is C(ω) from the other C(K) spaces?
Let us denote by C(α) the classical Banach space C(K) when K is the interval of ordinals [1,α] endowed with the order topology. In the present paper, we give an answer to a 1960 Bessaga and Pełczyński question by providing tight bounds for the Banach-Mazur distance between C(ω) and any other C(K) space which is isomorphic to it. More precisely, we obtain lower bounds L(n,k) and upper bounds U(n,k) on d(C(ω),C(ωⁿk)) such that U(n,k) - L(n,k) < 2 for all 1 ≤ n, k < ω.
How small are the sets where the metric projection fails to be continuous
How small is the phase space in quantum field theory ?
How smooth is almost every function in a Sobolev space?
We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.
How the μ-deformed Segal-Bargmann space gets two measures
This note explains how the two measures used to define the μ-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves a Macdonald function. Our primary result is that these densities are the solution of a system of ordinary differential equations which is naturally associated with this theory. We then solve this system and find the known densities as well as a "spurious" solution...
How to define "convex functions" on differentiable manifolds
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
How to define reasonably weighted Sobolev spaces
How to get rid of one of the weights in a two-weight Poincaré inequality?
We prove that if a Poincaré inequality with two different weights holds on every ball, then a Poincaré inequality with the same weight on both sides holds as well.
How to Obtain Vector-Valued Banach-Stone Theorems by Using M-Structure Methods.
How to solve an operator equation.
This article summarizes a series of lectures delivered at the Mathematics Department of the University of Leipzig, Germany, in April 1991, which were to overview techniques for solving operator equations on C*-algebras connected with methods developed in a Spanish-German research project on "Structure and Applications of C*-Algebras of Quotients" (SACQ). One of the researchers in this project was Professor Pere Menal until his unexpected death this April. To his memory this paper shall be dedicated....
Hp (Rn) is equidistributed with Lp (Rn).
Hull-minimal ideals in the Schwartz algebra of the Heisenberg group
For every closed subset C in the dual space of the Heisenberg group we describe via the Fourier transform the elements of the hull-minimal ideal j(C) of the Schwartz algebra and we show that in general for two closed subsets of the product of and is different from .
Hyers-Ulam constants of Hilbert spaces
The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.
Hyers-Ulam-Rassias stability of generalized derivations.
Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras.