On continuity of linear transformations commuting with generalized scalar operators (Preliminary communication)
A review of known decompositions of pairs of isometries is given. A new, finer decomposition and its properties are presented.
Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound of the spectrum of is an isolated point of ; (ii) (not necessarily an isolated point of with finite multiplicity) is an eigenvalue of .
We improve a result of Erb, concerning an uncertainty principle for orthogonal polynomials. The proof uses numerical range and a decomposition of some multiplication operators as a difference of orthogonal projections.
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.