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Journal of Operator Theory

Volume 82, Issue 1, Summer 2019  pp. 237-249.

Wiener--Hopf operators admit triangular factorization

Authors:  R.V. Bessonov
Author institution:St. Petersburg State University, St. Petersburg, Universitetskaya nab. 7, 199034, Russia \textit{and} St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Science, St. Petersburg, Fontanka 27, 191023, Russia

Summary: We prove that every positive bounded invertible Wiener--Hopf operator admits triangular factorization. This answers the question posed by L. Sakhnovich in 1994.

Keywords: Wiener-Hopf operators, canonical Hamiltonian systems, Szeg\"{o} theorem, triangular factorization

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