On similarity to contraction semigroups in Hilbert space

被引：2

作者：

Vu, QP ^{[1
]}

Yao, FY ^{[1
]}

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

SEMIGROUP FORUM | 1998年 / 56卷 / 02期

关键词：

Hilbert Space; Contraction Semigroup; Simultaneous Generalization;

D O I：

10.1007/PL00005941

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that if T(t) is a bounded, uniformly continuous, quasi-compact C-0-semigroup in Hilbert space, then T(t) is similar to a contraction semigroup. Analogously, if T is a power-bounded quasi-compact operator, then T is similar to a contraction. This latter fact is a simultaneous generalization of well known results of Sz.-Nagy and Rota. Some characterizations of bounded quasi-compact semigroups and power-bounded quasi-compact operators are also given.

引用

页码：197 / 204

页数：8

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