Representations of correlations of the $і [A, B] = f(A) + g(B)$ type

• Date: 1991
• Main Authors: Samoilenko , Yu. S., Shulman , V. S., Самойленко , Ю. С., Шульман , В. С.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1991
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9313
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

It is proved that all nontrivial representations of quadratic relation $i [A, B] = f(A) + g(B)$ with self-adjoint operators $A, B$ are unbounded if $f$ and $g$ are nonnegative; for any $f$ and $g$ this relation does not have nontrivial finite-dimensional representations and factor-representations of...