The Hadamard product in a crossed product C*-algebra

TL;DR

This paper introduces a generalized Hadamard product in reduced crossed product C*-algebras, extending known block Schur product results and providing a natural Stinespring representation.

Contribution

It defines a new Hadamard product for crossed product C*-algebras and shows its relation to the block Schur product, including a Stinespring representation.

Findings

Hadamard product generalizes convolution in crossed products

Block Schur product is a special case of the Hadamard product

The Hadamard product admits a natural Stinespring representation

Abstract

We show that for a C*-algebra A and a discrete group G with an action of G on A, the reduced crossed product C*-algebra possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. We show that this product has a natural Stinespring representation and we lift some known results on block Schur products to this setting, but we also show that the block Schur product is a special case of the Hadamard product in a crossed product algebra.