Matrix Young inequalities for the Hilbert–Schmidt norm
By Omar Hirzallah, F. Kıttaneh. 2000
94 citations recorded by the source corpus.
Abstract Let A,B, and X be n×n complex matrices such that A and B are positive semidefinite. If p,q>1 with 1 p + 1 q =1 , it is shown that ∥ 1 p A p X+ 1 q XB q ∥ 2 2 ⩾ 1 r 2 A p X−XB q 2 2 + AXB 2 2 , where r=max(p,q) and · 2 is the Hilbert–Schmidt norm. Generalizations and applications of this inequality are also considered.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/b08098dc599a1512a149c9c9ed5f106d2e0d8c92
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In Applied Mathematics
- Horst Alzer
- Alexander Kovacec
- C. da Fonseca
- F. Kıttaneh
- Yousef Manasrah
- T. Yamazaki
- Shigeru Furuichi
- Pintu Bhunia
In Computational Theory and Mathematics
- Alexander Kovacec
- Horst Alzer
- C. da Fonseca
- F. Kıttaneh
- Yousef Manasrah
- T. Yamazaki
- Shigeru Furuichi
- Pintu Bhunia
Citations in the corpus
- Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, unknown): “5 and [282].”
- Reverse Young and Heinz inequalities for matrices (2011, methodology): “Another refinement of (1.1) was given earlier by Hirzallah and Kittaneh [5]: ða b1 Þ2 þ r20 ffiffiffi a p ffiffiffi b p 2 ð aþ ð1 ÞbÞ2: ð1:4Þ The geometric mean ffiffiffiffiffi ab p and the arithmetic mean 12 ðaþ bÞ are famous examples of means of two positive real numbers.”
- The matrix arithmetic-geometric mean inequality revisited (2008, unknown): “Another paper on the inequality is [22].”
- Young-type inequalities and their matrix analogues (2015, background): “Our results extend some fresh inequalities established by Kittaneh, Manasrah, Hirzallah and Feng.”