Squaring a reverse AM-GM inequality
Studia Mathematica (2013)
- Volume: 215, Issue: 2, page 187-194
- ISSN: 0039-3223
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topMinghua Lin. "Squaring a reverse AM-GM inequality." Studia Mathematica 215.2 (2013): 187-194. <http://eudml.org/doc/285724>.
@article{MinghuaLin2013,
abstract = {
Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ,
Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B),
and
Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))²,
where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.
},
author = {Minghua Lin},
journal = {Studia Mathematica},
keywords = {operator inequalities; AM-GM inequality; positive linear maps; Hilbert space},
language = {eng},
number = {2},
pages = {187-194},
title = {Squaring a reverse AM-GM inequality},
url = {http://eudml.org/doc/285724},
volume = {215},
year = {2013},
}
TY - JOUR
AU - Minghua Lin
TI - Squaring a reverse AM-GM inequality
JO - Studia Mathematica
PY - 2013
VL - 215
IS - 2
SP - 187
EP - 194
AB -
Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ,
Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B),
and
Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))²,
where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.
LA - eng
KW - operator inequalities; AM-GM inequality; positive linear maps; Hilbert space
UR - http://eudml.org/doc/285724
ER -
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