一類線性算子半群的收斂性

禹曉紅, 宋曉秋, 李玉霞

(中國礦業(yè)大學 理學院,江蘇 徐州 221008)

一類線性算子半群的收斂性

禹曉紅, 宋曉秋, 李玉霞

(中國礦業(yè)大學 理學院,江蘇 徐州 221008)

為得到C0半群序列收斂于C0半群的條件,利用算子半群與無窮小生成元的關(guān)系,討論了C0半群的收斂性和算子序列逼近問題。在 Banach空間上,借助無窮小生成元的強收斂性得出其生成半群的強收斂性。借助定義有界線性算子Ln,將該結(jié)論推廣到了一般的Banach空間序列上,進一步完善了Banach空間上算子半群的收斂性理論。

C0半群;半群序列;無窮小生成元;收斂性;算子序列逼近;抽象柯西問題

0 引 言

設(shè)X表示Banach空間,B(X)表示X上全體有界線性算子構(gòu)成的Banach空間。

1 C0半群的收斂性

2 一般的 C0半群的收斂性

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Convergence of a kind of linear operator sem igroup

YU Xiaohong,SONG X iaoqiu,L I Yuxia
(College of Sciences,China University ofMining&Technology,Xuzhou 221008,China)

Aimed at enablingC0semigroup sequences to converge toC0semigroup,this paper discusses the convergence and operator series approximation ofC0semigroup using the relationship between operator semigroup and infinitesimal generator.In the space ofBanach,the strong convergence of infinitesimal generator results in the strong convergence of the generated semigroup.Besides,using the definition of a bounded linear operatorLn,makes it possible to extend the conclusion to the generalBanach space sequence,thus improving the convergence of semigroup in Banach space.

C0semigroup;semigroup sequence;infinitesimal generator;convergence;sequence of approximation operators;abstract Cauchy problem

O177.2

:A

1671-0118(2011)02-0161-02

2011-01-30

中央高?；究蒲袠I(yè)務費專項資金資助項目(2010LKSX08)

禹曉紅(1985-),女,山西省大同人,碩士,研究方向:應用泛函分析,E-mail:theyuxiaohong@126.com。

(編輯王 冬)