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On Clarkson-McCarthy inequalities for $ n$-tuples of operators

Author(s): Edward Kissin
Journal: Proc. Amer. Math. Soc. 135 (2007), 2483-2495.
MSC (2000): Primary 47A30; Secondary 46B20, 47B10
Posted: March 14, 2007
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Abstract: In this paper we obtain analogues of Clarkson-McCarthy inequalities for $ n$-tuples of operators from Schatten ideals $ C_p$. Using them, we extend the results of Bhatia and Kittaneh on inequalities for partitioned operators and for Cartesian decomposition of operators from $ C_p$.

References:

[AZ]
T. Ando and X. Zhan, Norm inequalities related to operator monotone functions, Math. Ann., 315(1999), 771-780. MR 1727183 (2000m:47008)

[BCL]
K. Ball, E.A. Carlen and E.H. Lieb, Sharp uniform convexity and smoothness inequalities for trace norms, Invent. Math., 115(1994), 463-482.MR 1262940 (95e:47027)

[B]
R. Bhatia, Matrix Analysis, Springer, New York, 1997.MR 1477662 (98i:15003)

[BH]
R. Bhatia and J.A.R. Holbrook, On the Clarkson-McCarthy inequalities, Math. Ann., 281(1988), 7-12. MR 0944598 (89m:47005)

[BK1]
R. Bhatia and F. Kittaneh, Norm inequalities for partitioned operators and applications, Math. Ann. 287 (1990), 719-726.MR 1066826 (91f:47010)

[BK2]
R. Bhatia and F. Kittaneh, Cartesian decompositions and Schatten norms, Linear Algebra and Appl., 318(2000), 109-116.MR 1787227 (2002k:47021)

[BK3]
R. Bhatia and F. Kittaneh, Clarkson inequalities with several operators, Bull. London Math. Soc., 36(2004), 820-832.MR 2083758 (2005m:47015)

[GK]
I. C. Gohberg and M.G. Krein, Introduction to the theory of linear non-selfadjoint operators in Hilbert space, Nauka, Moscow, 1965.MR 0220070 (36:3137)

[HK]
O. Hirzallah and F. Kittaneh, Non-commutative Clarkson inequalities for unitarily invariant norms, Pacific J. Math., 202(2002), 363-369.MR 1887770 (2003a:47020)

[M]
C.A. McCarthy, $ c_{p},$ Isr. J. Math., 5 (1967), 249-271.MR 0225140 (37:735)

[S]
B. Simon, Trace ideals and their applications, Cambridge University Press, 1979.MR 0541149 (80k:47048)

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Additional Information:

Edward Kissin
Affiliation: Department of Computing, Communications Technology and Mathematics, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, Great Britain
Email: e.kissin@londonmet.ac.uk

DOI: 10.1090/S0002-9939-07-08710-2
PII: S 0002-9939(07)08710-2
Received by editor(s): November 22, 2005 and, in revised form March 13, 2006
Posted: March 14, 2007
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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