检索结果-南通市图书馆

THE(U+K)-ORBITS OF ESSENTIALLY NORMAL operatorS AND THEIR STRONG IRREDUCIBILITY

在线全文

学校读者我要写书评

暂无评论

引用

Chinese Annals of Mathematics,Series B 1998年第2期19卷 217-228页

作者： JI YOUQING JIANG CHUNLAN Institute of Mathematics Jilin University Changchun 130023 China

The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation.... 详细信息

关键词： strongly irreducible operator Compact perturbation Normal operator

K_0-group and similarity of operator weighted shifts

在线全文

学校读者我要写书评

暂无评论

引用

Science China Mathematics 2012年第7期55卷 1441-1448页

作者： LIJueXian SchoolofMathematics LiaoningUniversityShenyang110036China

By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed by Cao et al. in 1999. Moreover, we discuss the relations between similarity and quasi-similarity for operator weighted shifts.

关键词： operator weighted shift strongly irreducible operator K0-group Lie algebra

Jordanian Canonical Form Theory in an Infinite Dimensional operator Algebra

在线全文

学校读者我要写书评

暂无评论

引用

Northeastern Mathematical Journal 2001年第3期17卷 265-268页

作者：纪友清孙善利 DepartmentofMathematics JilinUniversityChangchun130012DepartmentofMathematicsZhongshanUniversity

Let B(H) be the algebra of bounded linear operators acting on a separable Hilbert space *** operator T in B(H) is said to be strongly irreducible (see [1]), denoted by T ∈ (SI), if it is not similar to any reducible operator (see [2]). If the dimension of His finite, B(H) may be regarded as an n × n matrix algebra. Inthis case, T ∈(SI) if and only if T is similar to a Jordanian block. Jordanian canonical form theorem is one of the most important theorems in matrix theory. The Jordanian canonical form gives the complete set of similarity invariants of matrices. If the dimension of H is infinite, can we find an analogue of the Jordanian canonical form theorem in B(H)? First of all, we must know what is the analogue of the Jordanian block. Z. J. Jiang[3] thought of that the strongly irreducible operator may be suitable one. D. A. Herrero and C. L. Jiang[4] obtained an approximative Jordanian canonical form theorem. Since a normal operator having no eigenvalues cannot be similarto the orthogonal direct sum of strongly irreducible operators, there is no analogue of the Jordanian canonical form theorem in B(H). Many significant work concerns some special subalgebras, not the whole operator algebra B(H). So, it is reasonable to try to set up canonical form theory in some special operator algebras.

关键词： strongly irreducible operator (SI) decomposition commutant