| 杜鸿科.关于控制算子的若干注记[J].数学研究及应用,1987,7(2):263~268 |
| 关于控制算子的若干注记 |
| Some Remarks On Dominant Operators |
| 投稿时间：1983-06-08 |
| DOI：10.3770/j.issn:1000-341X.1987.02.015 |
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| Let B(H) be the set of all bounded linear operators on a Hilbert space H. An operator T∈B(H) is called dominant if (T-λ)(T-λ)*≤Mλ2(T-λ)*(T-λ),?λ∈C.The numerical range of T is difined by W (T) = {(Tx, x): ‖x‖ = 1, x∈H}. In Section 1 some new characteristic of dominant operators are given. If C = AB - BA, we prove that O∈W(C)- then A is a dominart or φ-quasihy ponor-mal. In Section 2 we prove that O∈σe(△Aσ) if A is a dominant, where(?), we also prove that if A∈B(H) is a norm attaining Ф-quasihyponormal, then A has a non-trivial invariant subspace. In Section 3 we discuss the closeness of the range of bounded linear operator FAB:X→AX-XB, and prove that R(δA)∩{A}′∩{An}′=0, where δA:X→AX-XA. |
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