scholarly journals Reverses and variations of Heinz inequality

2014 ◽  
Vol 63 (10) ◽  
pp. 1972-1980 ◽  
Author(s):  
Mojtaba Bakherad ◽  
Mohammad Sal Moslehian
Keyword(s):  
Heinz Inequality

A New Proof of an Inequality of Heinz

1964 ◽  
Vol 7 (1) ◽  
pp. 97-100
Author(s):  
P. S. Bullen
Keyword(s):  
Convexity Theorem ◽  
Heinz Inequality ◽  
Measure Spaces

In a recent paper, [l], Dixmier has proved Heinz' inequality by deducing it from a lemma due to Thorin. In this note it is proved directly from a convexity theorem.Let(M(k), ℳ(k), μ(k)), k = 0, …, n, be measure spaces and Lq(k) (M(k), ℳ(k), μ(k)) be all the functions on M(k) such that

scholarly journals Norm inequalities equivalent to Heinz inequality

1993 ◽  
Vol 118 (3) ◽  
pp. 827-827 ◽  
Author(s):  
Junichi Fujii ◽  
Masatoshi Fujii ◽  
Takayuki Furuta ◽  
Ritsuo Nakamoto
Keyword(s):  
Heinz Inequality ◽  
Norm Inequalities

scholarly journals Geometrical significance of the Löwner-Heinz inequality

1999 ◽  
Vol 128 (4) ◽  
pp. 1031-1037 ◽  
Author(s):  
E. Andruchow ◽  
G. Corach ◽  
D. Stojanoff
Keyword(s):  
Heinz Inequality ◽  
Geometrical Significance

A certain generalization of the Heinz inequality for positive operators

2016 ◽  
Vol 27 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Hideki Kosaki
Keyword(s):  
Positive Operators ◽  
Unitarily Invariant Norm ◽  
Heinz Inequality ◽  
Norm Inequalities ◽  
Invariant Norm

Norm inequalities of the form [Formula: see text] with [Formula: see text] and [Formula: see text] are studied. Here, [Formula: see text] are operators with [Formula: see text] and [Formula: see text] is an arbitrary unitarily invariant norm. We show that the inequality holds true if and only if [Formula: see text].

scholarly journals NORM INEQUALITIES EQUIVALENT TO LÖWNER-HEINZ THEOREM

1989 ◽  
Vol 01 (01) ◽  
pp. 135-137 ◽  
Author(s):  
TAKAYUKI FURUTA
Keyword(s):  
Heinz Inequality ◽  
Norm Inequalities

We give several norm inequalities equivalent to the famous Löwner-Heinz inequality.

A Converse of the Loewner–Heinz Inequality, Geometric Mean and Spectral Order

2014 ◽  
Vol 57 (2) ◽  
pp. 565-571 ◽  
Author(s):  
Mitsuru Uchiyama
Keyword(s):  
Real Number ◽  
Geometric Mean ◽  
Heinz Inequality ◽  
Spectral Order ◽  
Adjoint Operators

AbstractLet A, B be non-negative bounded self-adjoint operators, and let a be a real number such that 0 < a < 1. The Loewner–Heinz inequality means that A ≤ B implies that Aa ≦ Ba. We show that A ≤ B if and only if (A + λ)a ≦ (B + λ)a for every λ > 0. We then apply this to the geometric mean and spectral order.

scholarly journals Further refinements of the Heinz inequality

2014 ◽  
Vol 447 ◽  
pp. 26-37 ◽  
Author(s):  
Rupinderjit Kaur ◽  
Mohammad Sal Moslehian ◽  
Mandeep Singh ◽  
Cristian Conde
Keyword(s):  
Heinz Inequality
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