Wave operators and similarity for some non-selfadjoint operators
Wave operators and similarity for some non-selfadjoint operators
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DOI：
10.1007/978-3-642-85997-7_16
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发表时间：
1966-06
影响因子：
1.4
通讯作者：
Tosio Kato
中科院分区：
文献类型：
--
作者：
Tosio Kato
The purpose of the present paper is to develop a new method for establishing the similarity of a perturbed operatorT(ϰ), formally given byT+ ϰV, to the unperturbed operatorT. It is basically a “small perturbation” theory, since the parameter ϰ is assumed to be sufficiently small. Otherwise the setting of the problem is rather general;TorVneed not be symmetric or bounded, although they are assumed to act in a separable Hilbert space r and ϰ need not be real. The basic assumptions are that the spectrum ofTis a subset of the real axis, thatVcan be written formally asV=B*A, whereAisT-smoothandBisT*-smooth (see Definition 1.2), and thatA(T− ζ)−1B* is uniformly bounded for nonreal ζ. HereAandBare (in general unbounded) operators from r to another Hilbert space r′ (r′ = r is permitted). Strictly speaking, we are dealing with a certain extensionT(ϰ) ofT+ ϰB*A, which is uniquely determined byT,A, andB;T(ϰ) =T+ ϰB*Ais true ifAandBare bounded1).
