On the double unitary equivalence of operators (Q1387485)

In [\textit{Ma Jipu}, Sci. China, Ser. A 39, No. 12, 1258-1267 (1996; Zbl 0867.47013)] for the subspaces of Hilbert spaces \(H\) the concept of equivalence and a generalized dimension are introduced. We introduce a concept of double unitary equivalence from the singular decomposition of a matrix. In this note, we get the conditions of double unitary equivalent operators. Some general results are obtained.