A note on equicontinuity of families of operators and automorphisms

几乎等度连续性的积分刻画

An integral characterization of almost equicontinuity

通过积分截断平移条件刻画了有限测度子集上实值可测函数族的逐点几乎等度连续性，并给出反例说明有限测度和截断条件的必要性。

Natural proof of the characterization of relatively compact families in $L^p-$spaces on locally compact groups

In the paper we look for an elegant proof of the characterization of relatively compact families in $L^p-$spaces. At first glance, the suggested approach may seem convoluted and lengthy, but we spare no effort to argue that our proof is in fact more natural than the ones existent in the literature. The key idea is that the three properties which characterize relative compactness in $L^p-$spaces ($L^p-$boundedness, $L^p-$equicontinuity and $L^p-$equivanishing) are "preserved" (or rather "inherited") when the family $\Ffamily\subset L^p$ is convolved with a continuous and compactly supported fun…

Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras

This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense; i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.

Characterization of the Hilbert ball by its automorphism group

Let $Ω$ be a bounded, convex domain in a separable Hilbert space. The authors prove a version of the theorem of Bun Wong, which asserts that if such a domain admits an automorphism orbit accumulating at a strongly pseudoconvex boundary point then it is biholomorphic to the ball. Key ingredients in the proof are a new localization argument using holomorphic peaking functions and the use of new ``normal families'' arguments in the construction of the limit biholomorphism.

Calderón-type inequalities for affine frames

We prove sharp upper and lower bounds for generalized Calderón's sums associated to frames on LCA groups generated by affine actions of cocompact subgroup translations and general measurable families of automorphisms. The proof makes use of techniques of analysis on metric spaces, and relies on a counting estimate of lattice points inside metric balls. We will deduce as special cases Calderón-type inequalities for families of expanding automorphisms as well as for LCA-Gabor systems.