On the structure of a semigroup of operators with finite-dimensional ranges

被引：0

作者：

A. V. Pechkurov

机构：

[1] Voronezh State University,

来源：

Mathematical Notes | 2012年 / 91卷

关键词：

operator semigroup; strong continuity; complex Banach space; Banach algebra; spectrum of an operator; bounded linear operator;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In the present paper, we describe the structure of a strongly continuous operator semigroup T(t) (where T: ℝ+ → End X and X is a complex Banach space) for which ImT(t) is a finite-dimensional space for all t > 0. It is proved that such a semigroup is always the direct sum of a zero semigroup and a semigroup acting in a finite-dimensional space. As examples of applications, we discuss differential equations containing linear relations, orbits of a special form, and the possibility of embedding an operator in a C0-semigroup.

引用

页码：231 / 242

页数：11

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[6]

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[7]

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