| Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems |
| |
| 引用本文： | V. A. KHATSKEVICH V.A. SENDEROV. Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems[J]. 数学学报(英文版), 2006, 22(6): 1687-1694. DOI: 10.1007/s10114-005-0694-2 |
| |
| 作者姓名： | V. A. KHATSKEVICH V.A. SENDEROV |
| |
| 作者单位： | [1]Braude College, College Campus P. O. Box 78, Karmiel 21982, Israel [2]23-2-156, Pyatnitskoe highway, Moscow, 125430, Russia |
| |
| 摘 要： | The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.
|
| 关 键 词： | 紧性 凸性 线性分数关系 算子球 Krein空间 |
| 收稿时间： | 2004-08-12 |
| 修稿时间： | 2004-08-122005-01-05 |
Fractional–Linear Transformations of Operator Balls; Applications to Dynamical Systems |
| |
| V. A. Khatskevich,V. A. Senderov. Fractional–Linear Transformations of Operator Balls; Applications to Dynamical Systems[J]. Acta Mathematica Sinica(English Series), 2006, 22(6): 1687-1694. DOI: 10.1007/s10114-005-0694-2 |
| |
| Authors: | V. A. Khatskevich V. A. Senderov |
| |
| Affiliation: | (1) Braude College, College Campus, 78, Karmiel 21982, Israel;(2) 23–2–156, Pyatnitskoe highway, Moscow, 125430, Russia |
| |
| Abstract: | The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by “smooth” operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results. |
| |
| Keywords: | Compactness Convexity Linear fractional relation Operator ball Krein space |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
|
