[1]史平.关于N.Salinas的一个问题[J].东南大学学报(自然科学版),1988,18(5):8-15.[doi:10.3969/j.issn.1001-0505.1988.05.002]
 Shi Ping (Department of Mathematics and Mechanics).On a Problem of N. Salinas[J].Journal of Southeast University (Natural Science Edition),1988,18(5):8-15.[doi:10.3969/j.issn.1001-0505.1988.05.002]
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关于N.Salinas的一个问题()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
18
期数:
1988年第5期
页码:
8-15
栏目:
本刊信息
出版日期:
1988-09-20

文章信息/Info

Title:
On a Problem of N. Salinas
作者:
史平
南京工学院数学力学系
Author(s):
Shi Ping (Department of Mathematics and Mechanics)
关键词:
交换(半)亚正规算子组 Taylor联合谱和联合谱
Keywords:
commuting n-tuples of (semi) hyponormal operators Taylor’s joint spectra joint spectra
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1988.05.002
摘要:
本文主要讨论N.Salinas提出的一个问题:设T=(T_1,T_2…,T_n)是复Hilbert空间H上的交换n-亚正规算子组,是否有: (ⅰ) (ⅱ) δ(T-μ)=dist(μ,σ_l(T)),μ∈C^n?证明了对于一类交换半亚正规算子组,问题(ⅰ)和(ⅱ)成立。在一般情况下,给出问题(ⅰ)以否定回答。作为一个应用指出:即使在交换算子组的Taylor联合谱条件下,也存在交换n-亚正规算子组T(n≥=2),使其中σT(T)表示算子组T的J.L.Taylor联合谱。
Abstract:
This paper presents a discussion on a problem suggested by N. Salinas (J. Operator Theory, Vol. 10, 1983), i. e., if T=(T_1, T_2,…,T_n) is a commuting n-tuple of hyponormal operators on a complex Hilbert space H, do we have (ⅰ) (ⅱ) δ(T-μ)=dist(μ,σ_l,(T)),μ∈C^n ? It is proved that the proplems (ⅰ) and (ⅱ) are both true for some commuting n-tuples of semihyponormal operators. In general case, the problem (ⅰ) has a negative answer. As an application, we point out that there exists a commuting n-tuple of hyponormal operators T (n≥2), such that, where σ_T (T) denotes J. L. Taylor’s joint spectrum of T, even if the condition of Taylor’s joint spectra of T is given.
更新日期/Last Update: 2013-04-30