A characterization of commutators with Hilbert transforms

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...

Two-dimensional Hilbert Transforms'

A Characterization of Product BMO by Commutators

Here R+ denotes the upper half-plane and BMO(R 2 +×R 2 +) is defined to be the dual of the realvariable Hardy space H on the product domain R+×R 2 +. There are several equivalent ways to define this latter space and the reader is referred to [5] for the various characterizations. We will be more interested in the biholomorphic analogue of H, which can be defined in terms of the boundary values ...

Singular value inequalities for commutators of Hilbert space operators

Article history: Received 25 July 2008 Accepted 16 December 2008 Available online 30 January 2009 Submitted by R.A. Brualdi AMS classification: 47A30 47A63 47B10 47B15 47B47

Generalized multidimensional Hilbert transforms in Clifford analysis

During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...