ABSTRACT
Let Â, A ^ , B ^ , C ^ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn10_1.tif"/> Ĉ be arbitrary linear operators. Prove that
[ A ^ B ^ , C ^ ] = [ A ^ , C ^ ] B ^ + A ^ [ B ^ , C ^ ] , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn10_2.tif"/>
[ A ^ , [ B ^ , C ^ ] ] + [ B ^ , [ C ^ , A ^ ] ] + [ C ^ , [ A ^ , B ^ ] ] = 0. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn10_3.tif"/>
