On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Compact Operators on Hilbert Space

Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most imitate the more familiar linear algebra of finite-dimensional operator theory. In addition, these are of considerable practical value and importance. We prove a spectral theorem for self-adjoint operators with minimal fuss. Thus, we do not invoke broader discussions of properties of spectr...

Hankel Operators on Hilbert Space

commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...

On an inequality for operators on Hilbert space

On Commutators of Operators on Hilbert Space

1. In this note we first generalize a result of P. R. Halmos [3] concerning commutators of (bounded ) operators on Hubert space. Then we obtain some partial results on a problem of commutators in von Neumann algebras which is closely related to another problem raised by Halmos in [4]. Let 3C be any (infinite-dimensional) Hubert space, and let £(3C) denote the algebra of all bounded operators on...