On \(\sigma\)-finite integrals on \(C^*\)-algebras (Q909206)

For a given strictly positive element a of a \(\sigma\)-unital \(C^*\)- algebra A, the author constructs a dense hereditary *-subalgebra \(C_{00}(A)\), which may be regarded as a non-commutative analogue of the algebra of continuous functions with compact support. \(\sigma\)-finite integrals on \(C_{00}(A)\) are considered and associated \(L^ 1\)-spaces are constructed. Some noncommutative versions of measure theoretic theorems are proved.