A determinant formula for Toeplitz operators associated to a minimal flow

TL;DR

This paper introduces a determinant formula for Toeplitz operators linked to minimal flows, connecting it to algebraic K-theory and providing a new analytical tool for operator algebras.

Contribution

It defines a novel determinant on the Toeplitz algebra associated with minimal flows and relates it to the algebraic K-theory of functions on the space.

Findings

Derived a determinant formula in terms of symbols

Linked the determinant to algebraic K-theory

Provided insights into the structure of Toeplitz algebras

Abstract

We define a determinant on the Toeplitz algebra associated to a minimal flow, give a formula for this determinant in terms of symbols, and show that this determinant can be used to give information about the algebraic $K$-theory of functions on the underlying space.