On universal subsets of Banach spaces

We prove that to most of the known hypercyclic operators A on separable Banach spaces there exist compact (compact convex, compact connected) subsets K of E such that each compact (compact convex, compact connected) subset of E can be approximated with respect to Hausdorff's distance by for suitable . Received July 8, 1997, in final form October 17, 1997     

A note on a theorem of Raubenheimer and Rode

We prove the converse of Raubenheimer and Rode's Banach algebra version of the Perron-Frobenius Theorem.

     

Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.     

Dielectric relaxation of a short molecule in a liquid-crystalline solvent

Dielectric relaxation measurements of 5 mole % 4-n-hexyloxycyanobenzene (I) dissolved in 4-n-pentyloxyphenyl-trans-4-n-octylcyclohexylcarboxylate (II) were carried out from 1 kHz to 10 MHz in the nematic, smectic A and smectic B phases. The relaxation frequency of I parallel to the director is about 05 MHz in the S_Bphase and increases rapidly at the transition from S_B to S_A.     

Multicenter ligand transformations of thioureas on ruthenium clusters

The reaction of trirutheniumdodecacarbonyl with various thioureas was found to give, depending upon the substituents and the reaction conditions, a large variety of tri-, tetra-, penta-, and hexanuclear ruthenium clusters. The ligand systems observed in the products are derived from the thioureas employed; the fragmentation of the thiourea molecules involve N-H, C-S, C-H, and C-N activation processes.