| 书目名称 | Lie Algebras of Bounded Operators | | 编辑 | Daniel Beltiţă,Mihai Şabac | | 视频video | | | 丛书名称 | Operator Theory: Advances and Applications | | 图书封面 |  | | 描述 | In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar gener | | 出版日期 | Book 2001 | | 关键词 | Banach space; algebra; field; lie algebra; operator algebra; operator theory; spectral theory; transformati | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-8332-0 | | isbn_softcover | 978-3-0348-9520-0 | | isbn_ebook | 978-3-0348-8332-0Series ISSN 0255-0156 Series E-ISSN 2296-4878 | | issn_series | 0255-0156 | | copyright | Birkhäuser Verlag 2001 |
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发表于 2025-3-21 17:36:31
