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Алгебра и анализ, 1993, том 5, выпуск 6, страницы 69–96
(Mi aa415)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Статьи
Classification of finite-dimensional algebras generated by the calkin image of a composition operator on $L^p$ with weight
A. Böttcher, H. Heidler Technische Universität Chemnitz, Fakultät für Mathematik
Аннотация:
Given a countable infinite set $X$ and a weight $\mu\colon X\to(0,\infty)$, we denote by $l_{\mu}^p(X)$ the Banach space of all functions $f\colon X\to\mathbb C$ such that $\sum_{x\in X}|f(x)|^p\mu(x)<\infty$. The composition operator $C_a$ on $l_{\mu}^p(X)$ induced by a self-map $a\colon X\to X$ is defined by $(C_af)(x)=f(a(x))$. We establish a criterion for $C_a$ to be essentially algebraic, i.e., for the existence of a polynomial $q(z)$ such that $q(C_a)$ is compact. The polynomial $q(z)$ of minimal degree with this property is referred to as the essentially characteristic polynomial of $C_a$. We provide a list of all polynomials that may be the essentially characteristic polynomial of some composition operator on $l_{\mu}^p(X)$, which results in a complete classification of the finite-dimensional algebras generated by the Calkin image of a single composition operator on $l_{\mu}^p(X)$.
Ключевые слова:
composition operators, finite-dimensional algebras, algebraic operators, Calkin algebra.
Поступила в редакцию: 13.04.1993
Образец цитирования:
A. Böttcher, H. Heidler, “Classification of finite-dimensional algebras generated by the calkin image of a composition operator on $L^p$ with weight”, Алгебра и анализ, 5:6 (1993), 69–96; St. Petersburg Math. J., 5:6 (1994), 1099–1119
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa415 https://www.mathnet.ru/rus/aa/v5/i6/p69
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Страница аннотации: | 361 | PDF полного текста: | 132 | Первая страница: | 1 |
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