TY - JOUR
T1 - CONSTRUCTIONS OF MINIMAL HERMITIAN MATRICES RELATED TO A C*-SUBALGEBRA OF Mn(C)
AU - Zhang, Ying
AU - Jiang, Lining
AU - Han, Yongheng
N1 - Publisher Copyright:
© 2022 American Mathematical Society.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - This paper provides a constructive method using unitary diagonalizable elements to obtain all hermitian matrices A in Mn(C) such that ∥A∥ = Bmin ∈B ∥A + B∥, where B is a C*-subalgebra of Mn(C), ∥ · ∥ denotes the operator norm. Such an A is called B-minimal. Moreover, for a C*-subalgebra B determined by a conditional expectation from Mn(C) onto it, this paper constructs ∅ki=1 Bminimal hermitian matrices in Mkn(C) through B-minimal hermitian matrices in Mn(C), and gets a dominated condition that the matrix  = diag(A1, A2, · · ·, Ak) is ∅ki=1 B-minimal if and only if ∥Â∥ ≤ ∥As∥ for some s ∈ (1, 2, · · ·, k) and As is B-minimal, where Ai(1 ≤ i ≤ k) are hermitian matrices in Mn(C).
AB - This paper provides a constructive method using unitary diagonalizable elements to obtain all hermitian matrices A in Mn(C) such that ∥A∥ = Bmin ∈B ∥A + B∥, where B is a C*-subalgebra of Mn(C), ∥ · ∥ denotes the operator norm. Such an A is called B-minimal. Moreover, for a C*-subalgebra B determined by a conditional expectation from Mn(C) onto it, this paper constructs ∅ki=1 Bminimal hermitian matrices in Mkn(C) through B-minimal hermitian matrices in Mn(C), and gets a dominated condition that the matrix  = diag(A1, A2, · · ·, Ak) is ∅ki=1 B-minimal if and only if ∥Â∥ ≤ ∥As∥ for some s ∈ (1, 2, · · ·, k) and As is B-minimal, where Ai(1 ≤ i ≤ k) are hermitian matrices in Mn(C).
KW - Minimal hermitian matrix
KW - conditional expectation
UR - http://www.scopus.com/inward/record.url?scp=85142152652&partnerID=8YFLogxK
U2 - 10.1090/proc/16130
DO - 10.1090/proc/16130
M3 - Article
AN - SCOPUS:85142152652
SN - 0002-9939
VL - 151
SP - 73
EP - 84
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -