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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Cauchy-Schwarz and means inequalities for elementary operators into norm ideals


Author: Danko R. Jocić
Journal: Proc. Amer. Math. Soc. 126 (1998), 2705-2711
MSC (1991): Primary 47A30; Secondary 47B05, 47B10, 47B15
DOI: https://doi.org/10.1090/S0002-9939-98-04342-1
MathSciNet review: 1451812
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Abstract: The Cauchy-Schwarz norm inequality for normal elementary operators \[ \left \Vvert \sum _{n=1}^\infty A_nXB_n \right \Vvert \leq \left \Vvert (\sum _{n=1}^\infty A_n^*A_n)^{1/2}X (\sum _{n=1}^\infty B_n^*B_n)^{1/2} \right \Vvert , \] implies a means inequality for generalized normal derivations \[ \left \Vvert \frac {AX+XB}2 \right \Vvert \leq \Vvert X \Vvert ^{1-\frac 1r} \left \Vvert \frac {|A|^rX+X|B|^r}2 \right \Vvert ^\frac 1r,\] for all $r\ge 2$, as well as an inequality for normal contractions $A$ and $B$ \[ \left \Vvert (I-A^*A) ^\frac 12X(I-B^*B)^\frac 12\right \Vvert \leq \Vvert X-AXB\Vvert , \] for all $X$ in $B(H)$ and for all unitarily invariant norms $\Vvert \cdot \Vvert .$


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Additional Information

Danko R. Jocić
Affiliation: University of Belgrade, Faculty of Mathematics, Studentski trg 16, P. O. Box 550, 11000 Belgrade, Yugoslavia
Email: jocic@matf.bg.ac.yu

Keywords: Unitarily invariant norms, Ky Fan dominance property.
Received by editor(s): March 12, 1996
Received by editor(s) in revised form: February 4, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society