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Weylness of 2 × 2 operator matrices
Author(s) -
Wu Xiufeng,
Huang Junjie,
Chen Alatancang
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600424
Subject(s) - mathematics , operator (biology) , separable space , element (criminal law) , hilbert space , pure mathematics , algebra over a field , mathematical analysis , biochemistry , chemistry , repressor , political science , transcription factor , law , gene
Let H and K be complex separable infinite‐dimensional Hilbert spaces. Given the operators A ∈ B ( H ) , B ∈ B ( K ) and C ∈ B ( K , H ) , we defineM X : = [ACXB]where X ∈ B ( H , K ) is an unknown element. In this paper, a necessary and sufficient condition is given for M X to be a right Weyl (left Weyl, or Weyl) operator for some X ∈ B ( H , K ) . Moreover, some relevant properties and illustrating examples are also given.
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