Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Extended electrochemical windows made accessible by room temperature ionic liquid/organic solvent electrolyte systems

The electrochemical windows of acetonitrile solutions doped with 0.1 m concentrations of several ionic liquids were examined by cyclic voltammetry at gold and platinum microelectrodes. These results were compared with those observed in the commonly used 0.1 m tetrabutylammonium perchlorate/acetonitrile system as well as with neat ionic liquids. The use of a trifluorotris(pentofluoroethyl)phosphate-based ionic liquid, specifically, as supporting electrolyte in acetonitrile solutions affords a wider anodic window, which is attributed to the high stability of the anionic component of these intrinsically conductive and thermally robust compounds.