On unitary equivalence to a self-adjoint or doubly–positive Hankel operator

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2022-01-01 DOI:10.1515/conop-2022-0132
R.T.W. Martin
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引用次数: 0

Abstract

Abstract Let A be a bounded, injective and self-adjoint linear operator on a complex separable Hilbert space. We prove that there is a pure isometry, V, so that AV > 0 and A is Hankel with respect to V, i.e. V*A = AV, if and only if A is not invertible. The isometry V can be chosen to be isomorphic to N ∈ ℕ ∪ {+∞} copies of the unilateral shift if A has spectral multiplicity at most N. We further show that the set of all isometries, V, so that A is Hankel with respect to V, are in bijection with the set of all closed, symmetric restrictions of A−1.
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关于自伴随或双正Hankel算子的幺正等价
设A是复可分Hilbert空间上的一个有界、内射、自伴随线性算子。我们证明存在一个纯等距,V,使得AV > 0和a是关于V的Hankel,即V* a = AV,当且仅当a不可逆。如果A的谱多重性不超过N,则可以选择等距V同构于N∈N∪{+∞}的单侧位移副本。我们进一步证明了使A相对于V是Hankel的所有等距集合V与A−1的所有闭对称限制集合双射。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
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