Non-commutative Neveu decomposition and associated ergodic theorems

Title: Non-commutative Neveu decomposition and associated ergodic theorems

Speaker:Diptesh Saha（Indian Statistical Institute,Delhi）

Time: Monday, May 13, 2024, 15:00-16:00

Location:Zoom Meeting ID: 439 550 2599; Passcode: 0513

Abstract:In ergodic theory, depending on the sense of convergence, there are mainly three different kinds ofergodic theorems, namely mean ergodic theorems (convergence in norm), pointwise ergodic theorems (a.e.convergence), and stochastic ergodic theorems (convergence in measure). To study Krengel’s stochasticergodic theorem for a (not necessarily measure preserving) dynamical system, Neveu decomposition isan essential tool.

In this talk we will discuss some of this theorems in the non-commutative setting. We will beginwith non-commutative Neveu decomposition. Then we will briefly discuss pointwise ergodic theorems innon-commutative-spaces associated to the dynamical system, whereis a von Neumannalgebra,is either a group of polynomial growth, or, or, or a finitely generated free group, andαdenotes the action ofon.

Finally, we combine the Neveu decomposition and the pointwise ergodic theorems discussed aboveto show a stochastic ergodic theorem. This is a joint work with Dr. Panchugopal Bikram.