# Type-zero ternary corners

## TL;DR

This paper explores the structure of ternary corners within TROs, focusing on the relationship between TROs and sub-TROs via conditional expectations, especially when partial isometries are involved.

## Contribution

It introduces a special class of bounded linear maps on TROs and examines their properties in the context of ternary corners and partial isometries.

## Key findings

- Characterization of ternary corners and their relation to TROs.
- Analysis of a special class of bounded linear maps on TROs.
- Insights into the structure when TROs contain partial isometries.

## Abstract

In this paper we discuss the relationship between a TRO $\mathcal{T}$ and a sub-TRO $\mathcal{S}$ that is the range of a TRO-conditional expectation on $\mathcal{T}$, a \textit{ternary corner}, by investigating a special class $\mathcal{D}$ of bounded linear maps on~$\mathcal{T}$. We pay particular attention to the case when the TROs contain partial isometries.

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Source: https://tomesphere.com/paper/1906.07553