Properties and applications of a conjugate transform on Schatten classes

Abstract

Abstract We study a “conjugate” transform on matrix spaces. For Laurent/Toeplitz operators such a transform is a way of realizing the Hilbert transform on the torus. We establish its operator norm on Schatten classes and discuss the possibility of its boundedness upon permutations. Applications in the Rademacher–Menshov inequality and iterative methods are also included.

Keywords

• Rademacher–Menshov
• Triangular truncation
• Hilbert transform
• Conjugate transform
• Gauss–Seidel