All Questions

Background: for a discrete abelian group $G$, a character of $G$ is a homomorphism $\chi:G\to \mathbf S^1$, $\mathbf S^1$ being the circle group $\{z\in \mathbb C:|z|=1\}$ with ordinary multiplication....

From the paper Halmos, Paul R., In general a measure preserving transformation is mixing, Ann. Math. (2) 45, 786-792 (1944). ZBL0063.01889. the following result is known: Let $(E,\Sigma, \mu)$ be a ...

All definitions used in this post are from Björklund, Kosloff, and Vaes - Ergodicity and type of nonsingular Bernoulli actions. This post is inspired by the beginning of Section 2.2 in the same paper, ...

In Theorem 3.4.6 of the 'Lecture notes on ergodic theory' by Jesse Peterson, it is shown that in a weak mixing extension, every almost periodic function is trivial. I have a doubt in the proof of this ...

Let $T_1,T_2:L^1([0,1],\mathrm{d}x)\to L^1([0,1],\mathrm{d}x)$ be positive mean-ergodic operators such that: For every $h:[0,1]\to \mathbb{R}_+$ we have that $$\int_0^1 T_1 h(x)\mathrm{d}x = \int_0^1 ...

Let $X$ be a Polish space, and $\mu$ a locally finite measure. Take any $p \in \{0\} \cup [1,\infty)$. We will say that a linear operator $T \colon L^p(\mu) \to L^p(\mu)$ has property $(\ast)$ if ...