We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

The following paper is devoted to the study of type I locally compact quantum groups. We show how various operators related modular theory Haar integrals on G and ˆG act level direct integrals. Using these results we derive a web implications between properties such as unimodularity or traciality also in detail two examples: discrete group ˆSUq(2) az+b group.

For binary systems with an unseen primary and a luminous secondary, the astrometric wobble of secondary could be used to study primary. With Gaia, it is possible measure mass black hole or neutron star companion (hereafter BH/NS-LC). Our aim provide method for predicting Gaia's ability in measuring BH/NS-LCs. We also tried estimate number solvable BH/NS-LCs using Gaia. realistic Markov chain Mo...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

In a previous article by the author and P. Wesolek, it was shown that compactly generated locally compact group $G$ admits finite normal series $(G_i)$ in which factors are compact, discrete or irreducible sense no closed subgroup of lies properly between $G_{i-1}$ $G_{i}$. present article, we generalize this to an analogous decomposition coset space $G/H$ with respect subgroups, where is $H$ g...

For each locally compact non-compact c-compact Abelian group G whose dual is an I-group and each compact Abelian group ,?J such that there is a one-to-one continous homomorphism from G onto a dense subgroup of Z, we show the existence of cocycles on Z whose associated unitary representations of G have purely singular continuous spectrum, as well as the existence of cocycles on Z whose associate...