Rotation methods in operator ergodic theory.
Let denote the space of infinite matrices for which for all with . We characterize the upper triangular positive matrices from , , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.
The paper can be understood as a completion of the -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear -difference equations. The -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice with . In addition to recalling the existing concepts of -regular variation and -rapid variation we introduce -regularly bounded functions and prove many related properties. The -Karamata theory is then...