2017/10/31 by Amitava Jamatia, Jamatia, Amitava
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1710.11331
openalex publication_date 2017/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that if A,B∈ \mathbbB( H ) be positive operators, then \beginaligned A#Bamp;≤ (1)/(1-2μ)A(1)/(2)Fμ( A-(1)/(2)BA-(1)/(2) )A(1)/(2)
amp; ≤ (1)/(2)[ A#B+Hμ( A,B ) ]
amp; ≤ (1)/(2)[ (1)/(1-2μ)A(1)/(2) Fμ( A-(1)/(2)BA-(1)/(2) )A(1)/(2)+Hμ( A,B ) ]
amp; ≤ ⋯ ≤ \frac12nA#B+\frac2n-12nHμ( A,B )
amp; ≤ \frac12n( 1-2μ)A(1)/(2)Fμ( A-(1)/(2)BA-(1)/(2) )A(1)/(2)+\frac2n-12nHμ( A,B )
amp; ≤ \frac12n+1A#B+\frac2n+1-12n+1Hμ( A,B )
amp; ≤ ⋯ ≤ Hμ( A,B ). \endaligned for each μ∈ [ 0,1 ]\backslash \ (1)/(2) \. As an application, we present several inequalities for unitarily invariant norms. Our results are refinements of some existing inequalities.