On Mean Ergodic Convergence in the Calkin Algebras

Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Ergodic Theoretic Characterization of Left Amenable Lau Algebras

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

On Ergodic Properties of Convolution Operators Associated with Compact Quantum Groups

Recent results of M. Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum groups. The classical ergodic theory was initially concerned with investigating the limits of iterations (or iterated averages) of certain transformations of a...