On one class of matrix topological \(^{\ast}\)-algebras (Q2784891)

Let \(\Phi=\operatorname {pr} \lim _{\tau \in T}H_{\tau}\) be a projective limit of a family \((H_{tau})_{\tau \in T}\) of complex Hilbert spaces. The space \(\Phi\) is called nuclear if for each \(\tau \in T\) there exists \({\tau}'\in T\) such that the embedding \(H_{{\tau}'}\to H_{\tau}\) is quasi-nuclear. The main theorem of the paper is the following.NEWLINENEWLINENEWLINELet \(U\) be a commutative topological nuclear integer (bounded, analytical) \(^{\ast}\)-algebra. Then the matrix algebra \(A=M_{n}(U)\) is also a topological nuclear integer (bounded, analytical) \(^{\ast}\)-algebra.