On the systems of finite weights on the algebra of bounded operators and corresponding translation invariant measures
The authors describe the class of translation invariant measures on the algebra \(B(H)\) of bounded linear operators on a Hilbert space \(H\) and some of its subalgebras. Indeed, the authors study the properties of countable additivity, \(\sigma\)-finiteness, local finiteness of the constructed measure \(\lambda\), and the invariance of this measure with respect to some transformations of the algebra \(A\) is considered. Furthermore, they investigate the operator intervals in the Jordan algebra \(B(H)^{sa}\) and obtain some new operator inequalities.
scientific article; zbMATH DE number 7139450
scientific article