JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 39-44.doi: 10.6040/j.issn.1671-9352.0.2020.421

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The left-star order for idempotent operators

HAO Hong-yan, LI Yuan*   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2021-08-09

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Abstract: It is investigated that the characterizations of all idempotent operators on Hilbert space H with respect to the left-star order, which is defined by A*A=A*B and R(A)⊆R(B). Let A and B be two idempotent operators, the equivalent condition of A*≤B and the representation of operator matrix form is given. Meanwhile, the existence and representation of A∨B(supremum)and A∧B(infimum)of the star order when A*≤B is discussed.

Key words: idempotent operator, left-star order, operator matrix

CLC Number: 

  • O153.1
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