Ideal Spaces of the Haagerup Tensor Product of Ternary Rings of Operators

TL;DR

This paper characterizes various ideal structures within the Haagerup tensor product of a ternary ring of operators and a C*-algebra, enhancing understanding of their algebraic properties.

Contribution

It provides a detailed characterization of primal, factorial, and Glimm ideals in the Haagerup tensor product of TROs and C*-algebras, a novel analysis in operator algebra theory.

Findings

Identifies primal ideals in the tensor product

Describes factorial ideal structure

Analyzes Glimm ideals in the tensor product

Abstract

We characterize the primal, factorial, and Glimm ideals of the Haagerup tensor product $V\otimes^{h} B$ of a TRO $V$ and a $C^{\ast}$-algebra $B$.