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An inequality for Hilbert-Schmidt norm

✍ Scribed by Huzihiro Araki; Shigeru Yamagami

Book ID
105405653
Publisher
Springer
Year
1981
Tongue
English
Weight
379 KB
Volume
81
Category
Article
ISSN
0010-3616

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Two types of commutator inequalities for the Hilbert-Schmidt norm are established. The first type of these inequalities is related to a classical inequality of Clarkson, and the second type is related to the unitary approximation of positive and invertible operators.  2002 Elsevier Science (USA)

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Let A, B, and X be n Γ— n complex matrices such that A and B are positive semidefinite. 2 , where r = max(p, q) and β€’ 2 is the Hilbert-Schmidt norm. Generalizations and applications of this inequality are also considered.