Browsing by Author "P.Y.Wu"

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弱收縮變換之雙不變子空間
(交大學刊編輯委員會, 1978-04)
吳培元
;
P.Y.Wu
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.
滿足Alg T=｛T｝'之線性變換
(交大學刊編輯委員會, 1976-04)
吳培元
;
P.Y.Wu
For a bound linear operator T on a Hilbert space let {T}', {T}'' and Alg T denote the commutant, the double commutant and the weakly closed algebra generated by T and 1, respectively. Assume that T is a completely non-unitary contrction with a scalar-valued characteristics function Ψ(λ). In this note we show that the condition that |Ψ(e^it)|=1 on a set of positive Lebseque measure implies that Alg T={T}'. Moreover, if Ψ(λ) is assumed to be outer, then these two conditions are equivalent. Our main result generalizes the well-known fact that the compressions of the shift satisfy Alg T={T}'.