Geodesic
Inequalities related to Schatten norm
Filomat, Tome 35 (2021) no. 13, p. 4495

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In this paper, we investigate the known operator inequalities for the p-Schatten norm and obtain some refinements of these inequalities when parameters taking values in different regions. Let A1, · · · ,An,B1, · · · ,Bn ∈ Bp(H) such that Σni, j=1A∗i B j = 0. Then p ≥ 2, p ≤ λ and µ ≥ 2, 21/p−µ/4n3/p−µ/4−1/2( n∑ i=1 ‖Ai‖4/µp + n∑ i=1 ‖Bi‖4/µp )µ/4 ≤ n2/p−1/2‖ n∑ i=1 |Ai|2 + n∑ i=1 |Bi|2‖1/2p/2 ≤ n2/p−2/λ( n∑ i, j=1 ‖Ai ± B j‖λp )1/λ. For 0 p ≤ 2, p ≥ λ > 0 and 0 µ ≤ 2, the inequalities are reversed. Moreover, we get some applications of our results
DOI : 10.2298/FIL2113495G
Classification : 47B20, 47A63
Keywords: p-Schatten norm, Operator inequality, Convexity, Concavity, Orthogonality 
Fugen Gao; Meng Li; Mengyu Tian. Inequalities related to Schatten norm. Filomat, Tome 35 (2021) no. 13, p. 4495 . doi: 10.2298/FIL2113495G
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     author = {Fugen Gao and Meng Li and Mengyu Tian},
     title = {Inequalities related to {Schatten} norm},
     journal = {Filomat},
     pages = {4495 },
     year = {2021},
     volume = {35},
     number = {13},
     doi = {10.2298/FIL2113495G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2113495G/}
}
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