We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product… Expand

We obtain some necessary or sufficient conditions for an operator on a complex separable Hilbert space to be expressible as a product of two normal operators. For example, it is shown that if T is… Expand

Denote by W(A) the numerical range of a bounded linear operator A. For two operators A and B (which may act on different Hilbert spaces), we study the relation between the inclusion relation… Expand

Abstract In this paper, we consider the problem of characterizing Hilbert space operators which are expressible as a sum of (finitely many) orthogonal projections. We obtain a special operator matrix… Expand