Operator Set of Nest Algebra in Direct Sums and Its Invertible Operators

Abstract:

      In this paper, we characterize the properties of X_N^φ, where X_N^φ is an operator set of nest algebra, and show that the direct sum of nest algebra is τ(N) = D_N⊕X_N^φ. We prove also that the invertible element of operators in D_N belongs to D_N. When the nest is a countable nest, we obtain that the invertible element of the operator T in τ(N) belongs to τ(N) if and only if φ(T) is invertible.