Matrix Young inequalities for the Hilbert–Schmidt norm

Hirzallah, Omar; Kittaneh, Fuad

doi:10.1016/s0024-3795(99)00270-0

Cited by 77 publications

(39 citation statements)

References 10 publications

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“…Based on the refined and reversed Young inequalities (1.5) and (1.6), Hirzallah and Kittaneh [4], and Kittaneh and Manasrah [7], respectively, proved that if A, B, X ∈ M n (C) such that A and B are positive semidefinite, then …”

Section: Some Inequalities For Unutarily Invariant Normsmentioning

confidence: 99%

Further Generalizations, Refinements, and Reverses of the Young and Heinz Inequalities

Al-Manasrah

Kittaneh

2016

Results Math

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Section: Some Inequalities For Unutarily Invariant Normsmentioning

confidence: 99%

Further Generalizations, Refinements, and Reverses of the Young and Heinz Inequalities

Al-Manasrah

Kittaneh

2016

Results Math

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“…where, for any B ∈ M n (C), Re B and Im B are the matrices For inequalities related to inequalities (8), (9), and (11), we refer to [4], [7], and [10]. Now we utilize the previous lemmas to prove our commutator inequalities that are associated with the polar decomposition.…”

Section: Lemma 2 Ifmentioning

confidence: 99%

Commutator inequalities associated with the polar decomposition

Kittaneh

2001

Proc. Amer. Math. Soc.

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“…[7] that it is true if a, b are Hilbert-Schmidt operators, and the norm is the Hilbert-Schmidt norm. Another nice paper, this time by M. Argerami and D. Farenick [3] proved that that it is also true for |a| p , |b| q nuclear operators, that is when the norm is the trace norm…”

Section: Introductionmentioning

confidence: 99%

Young’s (in)equality for compact operators

Larotonda

2016

Studia Math.

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If a, b are n × n matrices, Ando proved that Young's inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, thenLater, this result was extended for the singular values of a pair of compact operators acting on a Hilbert space by Erlijman, Farenick and Zeng. In this paper we prove that if a, b are compact operators, then equality holds in Young's inequality if and only if |a| p = |b| q , obtaining a complete characterization of such a, b in relation to other (operator norm) Young inequalities. Operator analogues of this elegant fact are considered, following the fundamental paper by T. Ando [1] for n × n matrices, and an extension for compact operators by J. Erlijman, * 2010 MSC. Primary 15A45, 47A30; Secondary 15A42, 47A63.

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Matrix Young inequalities for the Hilbert–Schmidt norm

Cited by 77 publications

References 10 publications

Further Generalizations, Refinements, and Reverses of the Young and Heinz Inequalities

Further Generalizations, Refinements, and Reverses of the Young and Heinz Inequalities

Commutator inequalities associated with the polar decomposition

Young’s (in)equality for compact operators

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