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Dimensional compactness in biequivalence vector spaces

J. Náter, P. Pulmann, Pavol Zlatoš (1992)

Commentationes Mathematicae Universitatis Carolinae

The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a π -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set s and classes of set functions s → Q ...

Estimations de Strichartz pour des perturbations à longue portée de l’opérateur de Schrodinger

Nicolas Burq (2001/2002)

Séminaire Équations aux dérivées partielles

On présente dans cet exposé une approche semi-classique déduite des résultats de N. Burq, P. Gérard et N. Tzvetkov [4] permettant de démontrer des inégalités de Strichartz pour un problème non captif. On retrouve ainsi des résultats de G. Staffilani et D. Tataru [16] (obtenus pour une perturbation de la métrique à support compact). On donne aussi des généralisations de ces résultats au cas d’une perturbation à longue portée

Generalized weak peripheral multiplicativity in algebras of Lipschitz functions

Antonio Jiménez-Vargas, Kristopher Lee, Aaron Luttman, Moisés Villegas-Vallecillos (2013)

Open Mathematics

Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all 𝕂 -valued Lipschitz functions on X - where 𝕂 is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that R a n π ( T 1 ( f ) T 2 ( g ) ) ∩ R a n π ( S 1 ( f ) S 2 ( g ) ) ≠ ∅ for all f, g ∈ Lip0(X),...

Hopf algebras of smooth functions on compact Lie groups

Eva C. Farkas (2000)

Commentationes Mathematicae Universitatis Carolinae

A C ∞ -Hopf algebra is a C ∞ -algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C ∞ -Hopf algebras which are given by the algebra C ∞ ( G ) of smooth functions on some compact Lie group G , thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

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