Isomorphism of some new Kadison–Singer algebras
摘要
Some new classes of Kadison-Singer lattices (KS-lattices) and Kadison-Singer algebras (KS-algebras) are constructed. These KS-lattices are determined by a given KS-lattice, some discrete nest of projections and one special projection. Some quantities for these lattices are used to classify these KS-algebras. It is shown that these KS-algebras are isometrically isomorphic if and only if they are unitarily equivalent if and only if they have the same quantities.