Open AccessInequalities for sector matrices and positive linear maps
Author(s) -
Fuping Tan,
Huimin Che
Publication year - 2019
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2019.5239
Subject(s) - mathematics , geometric mean , inequality , positive definite matrix , norm (philosophy) , weighted geometric mean , combinatorics , pure mathematics , statistics , mathematical analysis , eigenvalues and eigenvectors , physics , quantum mechanics , political science , law
Ando proved that if A, B are positive definite, then for any positive linear map Φ, it holds Φ(A#λB) ≤ Φ(A)#λΦ(B), where A#λB, 0 ≤ λ ≤ 1, means the weighted geometric mean of A, B. Using the recently defined geometric mean for accretive matrices, Ando’s result is extended to sector matrices. Some norm inequalities are considered as well.