|
Zapiski Nauchnykh Seminarov POMI, 2006, Volume 333, Pages 54–61
(Mi znsl241)
|
|
|
|
Commutators in model spaces
V. V. Kapustin St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
Let $\theta$ be an inner function, let $K_\theta=H^2\ominus\theta H^2$, and let $S_\theta\colon K_\theta\to K_\theta$ be defined by the formula $S_\theta f=P_\theta zf$, $f\in K_\theta$, where $P_\theta$ is the orthogonal projection of $H^2$ onto $K_\theta$. Consider the set $A$ of all trace class operators $L\colon K_\theta\to K_\theta$, $L=\sum(\cdot,u_n)v_n$, $\sum\|u_n\|\|v_n\|<\infty$ $(u_n,v_n\in K_\theta)$, such that $\sum\bar u_nv_n\in H^1_0$. It is shown that the trace class commutators of the form $XS_\theta-S_\theta X$ (where $X$ is a bounded linear operator on $K_\theta$) are dense in $A$ in the trace class norm.
Received: 27.07.2006
Citation:
V. V. Kapustin, “Commutators in model spaces”, Investigations on linear operators and function theory. Part 34, Zap. Nauchn. Sem. POMI, 333, POMI, St. Petersburg, 2006, 54–61; J. Math. Sci. (N. Y.), 141:5 (2007), 1538–1542
Linking options:
https://www.mathnet.ru/eng/znsl241 https://www.mathnet.ru/eng/znsl/v333/p54
|
Statistics & downloads: |
Abstract page: | 181 | Full-text PDF : | 54 | References: | 29 |
|