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.

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.