Cauchy-Schwarz and means inequalities

for elementary operators into norm ideals

Author:
Danko R. Jocic

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 | References | Similar Articles | Additional Information

Abstract: The Cauchy-Schwarz norm inequality for normal elementary operators

implies a means inequality for generalized normal derivations

for all , as well as an inequality for normal contractions and

for all in and for all unitarily invariant norms

**[BSh]**J. Bendat and S. Sherman,*Monotone and Convex Operator Functions,*Trans. Amer. Math. Soc.**79**(1955), 58-71. MR**18:588b****[BhD]**R. Bhatia and Ch. Davis,*More matrix forms of the arithmetic-geometric mean inequality,*SIAM J. Matrix. Anal. Appl.**14**(1993), 132-136. MR**94b:15017****[F83]**L. Fialkow,*Spectral properties of elementary operators,*Acta Sci. Math. (Szeged),**46**(1983), 269-282. MR**85h:47003****[F85]**L. Fialkow,*Spectral properties of elementary operators II,*Trans. Amer. Math. Soc.**290**(1985), 415-429. MR**86j:47005****[F87]**L. Fialkow,*The range inclusion problem for elementary operators,*Michigan J. Math.**34**(1987), 451-459. MR**89a:47052****[FL]**L. Fialkow and R. Loebl,*Elementary mappings into ideals of operators,*Illinois Journal Math. Vol**28**(1984), 555-578. MR**86g:47054****[GK]**I.C. Gohberg and M.G. Krein,*Introduction to the theory of linear nonselfadjoint operators,*Transl. Math. Monographs, vol.**18**, Amer. Math. Soc. Providence, R.I. 1969. MR**39:7447****[Ki]**F. Kittaneh,*Norm inequalities for fractional powers of positive operators ,*Lett. Math. Phys.**27**(1993), 279-285. MR**94e:47011****[LR]**G. Lumer and M. Rosenblum,*Linear operator equations,*Proc. Amer. Math. Soc.**10**(1959), 32-41. MR**21:2927****[McI]**A. McIntosh, A. Pryde and W. Ricker,*Estimates for the solution of operator equation*Operator Theory, Adv. & Appl., Vol.**20**, pp. 197-207. Birkhauser Verlag Basel 1988. MR**89k:47024****[Sch]**R. Schatten,*Norm Ideals of completely continuous operators,*Springer-Verlag, Berlin, 1960. MR**22:9878****[Si]**B. Simon,*Trace Ideals and their applications,*Cambridge University Press, 1979. MR**80k:47048****[W83]**G. Weiss,*An extension of the Fuglede commutativity theorem modulo the Hilbert-Schmidt class to the operators of the form ,*Trans. Amer. Math. Soc.**278**(1983), 1-20. MR**84e:47026**

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Additional Information

**Danko R. Jocic**

Affiliation:
University of Belgrade, Faculty of Mathematics, Studentski trg 16, P. O. Box 550, 11000 Belgrade, Yugoslavia

Email:
jocic@matf.bg.ac.yu

DOI:
https://doi.org/10.1090/S0002-9939-98-04342-1

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