Let X and Y be operators on Hilbert space, and let L be a nest of projections on the space. We consider the problem of finding an operator A in Alg L: such that A is Hilbert-Schmidt and such that AX = Y. A necessary and sufficient condition involving X,Y, and the projections in the lattice is found. We also indicate how the statements of the results can be modified so that the main theorem is t...

We shall show that B(H) can be represented by the strong closure of the linear span of the compounds of a fixed operator in B(H) and the rank one operators, composed only by the vectors of a certain orthonormal basis of H, in a nest algebra, even, under some assumption, in the radical of a nest algebra. 0. Notations, basic relationships, and introduction Throughout, the nonzero Hilbert space H ...

This paper is a comprehensive study of the nest representations for the free semigroupoid algebra LG of countable directed graph G as well as its norm-closed counterpart, the tensor algebra T (G). We prove that the finite dimensional nest representations separate the points in LG, and a fortiori, in T (G). The irreducible finite dimensional representations separate the points in LG if and only ...

The structure of graded triangular algebras T of arbitrary dimension are studied in this paper. This is motivated in part for the important role that triangular algebras play in the study of oriented graphs, upper triangular matrix algebras or nest algebras. It is shown that T decomposes as T = U + ( ∑ i∈I Ti), where U is an R-submodule contained in the 0-homogeneous component and any Ti a well...