Operator Categories I. T*-categories

TL;DR

This paper introduces T*-categories as a ternary extension of C*-categories, generalizes Gelfand-Naimark theorems to them, and explores their biduals, expanding the theoretical framework of operator categories.

Contribution

It presents the concept of T*-categories, extends key representation theorems, and analyzes biduals, providing a new mathematical structure in operator theory.

Findings

T*-categories generalize C*-categories using ternary structures

Gelfand-Naimark theorems are extended to T*-categories

Biduals of T*-categories are characterized

Abstract

T*-categories are introduced as a ternary generalization of C*-categories. Their linking C*-categories are constructed and the Gelfand-Naimark representation theorems of Zettl for C*-ternary rings and for W*-ternary rings, are generalized to T*-categories. Biduals of C*-categories and of T*-categories are considered.