Crossed product by an arbitrary endomorphism

TL;DR

This paper introduces a new construction of crossed products for unital C*-algebras driven by arbitrary endomorphisms, emphasizing the role of an ideal orthogonal to the kernel of the endomorphism.

Contribution

It develops a generalized crossed product construction that depends on both the endomorphism and an orthogonal ideal, extending previous frameworks.

Findings

The construction depends on the choice of an ideal orthogonal to Ker elta.

Provides a new approach to crossed products for arbitrary endomorphisms.

Highlights the importance of the ideal in the structure of the crossed product.

Abstract

Starting from an arbitrary endomorphism \delta of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\delta) but also on the choice of an ideal J orthogonal to Ker \delta.