# $\varphi$-contractibility and $\varphi$-Connes amenability coincide with some older notions

## TL;DR

This paper demonstrates that several notions of $\

## Contribution

It shows that various definitions of $\

## Key findings

- Different definitions of $\
- Older concepts are equivalent to newer ones

## Abstract

It is shown that various definitions of $\varphi$-Connes amenability as introduced independently in \cite{Gh-Ja, mah, Sh-Am}, are just rediscovering existing notions and presenting them in different ways. It is also proved that even $\varphi$-contractibility as defined in \cite{Sangani}, is equivalent to an older and simpler concept.