Norm inequalities related to clarkson inequalities

Citation data:

Electronic Journal of Linear Algebra, ISSN: 1081-3810, Vol: 34, Issue: 1, Page: 163-169

Publication Year:
2018
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DOI:
10.13001/1081-3810,1537-9582.3642; 10.13001/1081-3810,1537-9582.3528; 10.13001/1081-3810, 1537-9582.3200; 10.13001/1081-3810, 1537-9582.3649; 10.13001/1081-3810,1537-9582.3449; 10.13001/1081-3810,1537-9582.3530; 10.13001/1081-3810, 1537-9582.3741; 10.13001/1081-3810,1537-9582.3595; 10.13001/1081-3810, 1537-9582.3609; 10.13001/1081-3810, 1537-9582.3121; 10.13001/1081-3810, 1537-9582.2982; 10.13001/1081-3810, 1537-9582.3588; 10.13001/1081-3810,1537-9582.3416; 10.13001/1081-3810,1537-9582.3510; 10.13001/1081-3810, 1537-9582.3635; 10.13001/1081-3810, 1537-9582.3636; 10.13001/1081-3810, 1537-9582.3467; 10.13001/1081-3810, 1537-9582.3613; 10.13001/1081-3810, 1537-9582.3449; 10.13001/1081-3810, 1537-9582.3647; 10.13001/1081-3810, 1537-9582.3671; 10.13001/1081-3810, 1537-9582.3416; 10.13001/1081-3810, 1537-9582.3750; 10.13001/1081-3810, 1537-9582.3732; 10.13001/1081-3810, 1537-9582.3782; 10.13001/1081-3810, 1537-9582.3578; 10.13001/1081-3810, 1537-9582.3595; 10.13001/1081-3810, 1537-9582.3542; 10.13001/1081-3810, 1537-9582.3793; 10.13001/1081-3810, 1537-9582.3654; 10.13001/1081-3810, 1537-9582.3528; 10.13001/1081-3810, 1537-9582.3493; 10.13001/1081-3810, 1537-9582.3774; 10.13001/1081-3810, 1537-9582.3675; 10.13001/1081-3810, 1537-9582.3667; 10.13001/1081-3810, 1537-9582.3555; 10.13001/1081-3810, 1537-9582.3733; 10.13001/1081-3810, 1537-9582.3748; 10.13001/1081-3810, 1537-9582.3688; 10.13001/1081-3810, 1537-9582.3642; 10.13001/1081-3810, 1537-9582.3727; 10.13001/1081-3810, 1537-9582.3743; 10.13001/1081-3810, 1537-9582.3510; 10.13001/1081-3810, 1537-9582.3651; 10.13001/1081-3810, 1537-9582.3539; 10.13001/1081-3810, 1537-9582.3665; 10.13001/1081-3810, 1537-9582.3659; 10.13001/1081-3810, 1537-9582.3616; 10.13001/1081-3810, 1537-9582.3600; 10.13001/1081-3810, 1537-9582.3530; 10.13001/1081-3810, 1537-9582.3746
Author(s):
Aalipour, Ghodratollah; Abiad, Aida; Berikkyzy, Zhanar; Hogben, Leslie; Kenter, Franklin H.J.; Lin, Jephian C.-H.; Tait, Michael
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article description
Let A and B be n × n matrices. It is shown that if p = 2, 4 ≤ p < ∞, or 2 < p < 4, and both A + B, A − B are positive semidefinite, then) ( ∣ ∣ ‖A + B‖pp‖A‖pp − 2p − 2) − ‖B‖and if p = 2, 4 ≤ p < ∞, or 2 < p < 4, and both A, B are positive semidefinite, then) ∣ ‖A + B‖pp (‖A‖pp + (2− 2∣p) ∣‖A + B‖− ‖A − B‖These inequalities are reversed if p = 2, 1 ≤ p ≤3< p < 2, and both A + B, A − B are positive semidefinite, and if 3 p = 2, 1 ≤ p ≤3< p < 2, and both A, B are positive semidefinite, respectively. Commutative (or Lp) versions of these 3 inequalities are also considered.