The operator Fejer-Riesz theorem

Abstract

The Fejer-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrix- and operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum's operator generalization of the classical Fejer-Riesz theorem.

33 pages. To appear in the The Paul R. Halmos memorial volume in the series Operator Theory: Advances and Applications, published by Birhauser, edited by Sheldon Axler, Peter Rosenthal and Donald Sarason

References in corpus (1)

• Positive polynomials in scalar and matrix variables, the spectral theorem and optimization