大子代数中的极大幂零理想和代数同构

§ 1　Introduction and preliminariesLet Hbe a complex Hilbertspace,B(H) be the setof all linear bounded operators.A set Nofprojections on His called a nestif(1 ) Nistotally ordered by the usual oper-ator order,(2 ) Ncontains the zero operator0 and the identity operator I,and(3 ) givenany subset N0 N,the operators sup{ N:N∈N0 } and inf{ N:N∈ N0 } are both mem-bers of N.For N∈Nwith N>0 ,we define N- =sup{ N′∈N:N′

Maximal nilpotent ideals and isomorphisms of large subalgebras of nest algebras

Let N be a nest of projections on a Hilbert space H and ℐ (N) be the corresponding nest algebra. Let N be a large subalgebra of ℐ (N). It is proved that any maximal n-nilpotent ideal of A is in the form of A ∩ ℛ_ℱ, where ℱ is a finite subnest of N and ℛ_ℱ is the Jacobson radical of ℐ (ℱ). Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.