期刊
LINEAR ALGEBRA AND ITS APPLICATIONS
卷 617, 期 -, 页码 179-189出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2021.02.003
关键词
Sectorial matrices; Accretive-dissipative matrices; Singular values; Unitarily invariant norms; Minkowski's inequality and Young's inequality
This article discusses the restrictions on the numerical range of T under the condition of its polar decomposition, and provides related inequality conclusions.
Assume that the numerical range of T is an element of M-n is a subset of the sector S-alpha = {z is an element of C : Re(z) > 0, vertical bar Im(z)vertical bar <= tan(alpha)Re(z)}. It is proved that, if T = U vertical bar T vertical bar is the polar decomposition of T, then vertical bar T vertical bar <= sec(alpha) [Re(T)#U*Re(T)U]. Several consequences of this inequality are established, including singular value inequalities, unitarily invariant norm inequalities and sharp determinant inequalities. (C) 2021 Elsevier Inc. All rights reserved.
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