The Semi-Algebra Generated by a Compact Linear Operator
The Semi-Algebra Generated by a Compact Linear Operator
We prove that if t is a compact linear operator that is not quasi-nilpotent and is appropriately normalised, then the closed semi-algebra A(t) generated by t is locally compact. The theory of locally compact semi-algebras ( 2 ) is therefore applicable to A(t) , and we show that it can …