標題: 弱收縮變換之雙不變子空間
Bi-invariant Subspaces of Weak Constrictions
作者: 吳培元
P.Y.Wu
公開日期: Apr-1978
出版社: 交大學刊編輯委員會
摘要: For a bounded linear operator T acting on a complex, separable Hilbert space, let Lat T,Lat''T and Hyperlat T denote the lattices of invariant subspace, bi-invariant subspaces and hyperinvariant subspaces of T, respectively. In this paper we characterize the elements of Lat''T, in terms of the characteristic function of T, when T is a completely non-unitary weak contraction with finite defect indices. We show that if the defect indices of T are n <= and ΘT denotes the characteristic function of T , then a subspace in Lat T belongs to Lat''T if and only if the intermediate space of its corresponding regular factorization ΘT=Θ2 Θ1 is of dimension n.As corollaries, necessary and sufficient conditions that two of these lattices of subspaces be equal to each other are obtained.In particular, if T1, T2 are completely non-unitary C11 contractions with finite defect indices which are quasi-similar to each other, then Lat''T1 is isomorphic to Lat "T2.Whether this is true for weak contractions is still unknown.
URI: http://hdl.handle.net/11536/137607
期刊: 交通大學學報
The Journal of National Chiao Tung University
Volume: 4
起始頁: 45
結束頁: 47
Appears in Collections:The Journal of National Chiao Tung University


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