English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We show that a class of ergodic transformations on a probability measurespace $(X,\mu)$ extends to a representation of $\mathcal{B}(L^2(X,\mu))$ thatis both implemented by a Cuntz family and ergodic. This class contains severalknown examples, which are unified in this work.  During the analysis of the existence and uniqueness of such a Cuntz family wegive several results of individual interest. Most notably we prove adecomposition of $X$ for $N$-to-one local homeomorphisms that is connected tothe orthonormal basis of Hilbert modules. We remark that the trivial Hilbertmodule of the Cuntz algebra $\mathcal{O}_N$ does not have a well-definedHilbert module basis (moreover that it is unitarily equivalent to the modulesum $\sum_{i=1}^n \mathcal{O}_N$ for infinitely many $n \in \mathbb{N}$).

Ergodic extensions and Hilbert modules associated to endomorphisms of MASAS