On Clarkson-McCarthy inequalities for 𝑛-tuples of operators

Kissin, Edward

doi:10.1090/S0002-9939-07-08710-2

On Clarkson-McCarthy inequalities for $n$-tuples of operators
HTML articles powered by AMS MathViewer

by Edward Kissin PDF

Proc. Amer. Math. Soc. 135 (2007), 2483-2495 Request permission

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

Tsuyoshi Ando and Xingzhi Zhan, Norm inequalities related to operator monotone functions, Math. Ann. 315 (1999), no. 4, 771–780. MR 1727183, DOI 10.1007/s002080050335
Keith Ball, Eric A. Carlen, and Elliott H. Lieb, Sharp uniform convexity and smoothness inequalities for trace norms, Invent. Math. 115 (1994), no. 3, 463–482. MR 1262940, DOI 10.1007/BF01231769
Rajendra Bhatia, Matrix analysis, Graduate Texts in Mathematics, vol. 169, Springer-Verlag, New York, 1997. MR 1477662, DOI 10.1007/978-1-4612-0653-8
Rajendra Bhatia and John A. R. Holbrook, On the Clarkson-McCarthy inequalities, Math. Ann. 281 (1988), no. 1, 7–12. MR 944598, DOI 10.1007/BF01449211
Rajendra Bhatia and Fuad Kittaneh, Norm inequalities for partitioned operators and an application, Math. Ann. 287 (1990), no. 4, 719–726. MR 1066826, DOI 10.1007/BF01446925
Rajendra Bhatia and Fuad Kittaneh, Cartesian decompositions and Schatten norms, Linear Algebra Appl. 318 (2000), no. 1-3, 109–116. MR 1787227, DOI 10.1016/S0024-3795(00)00206-8
Rajendra Bhatia and Fuad Kittaneh, Clarkson inequalities with several operators, Bull. London Math. Soc. 36 (2004), no. 6, 820–832. MR 2083758, DOI 10.1112/S0024609304003467
I. C. Gohberg and M. G. Kreĭn, Vvedenie v teoriyu lineĭ nykh nesamosopryazhennykh operatorov v gil′bertovom prostranstve, Izdat. “Nauka”, Moscow, 1965 (Russian). MR 0220070
Omar Hirzallah and Fuad Kittaneh, Non-commutative Clarkson inequalities for unitarily invariant norms, Pacific J. Math. 202 (2002), no. 2, 363–369. MR 1887770, DOI 10.2140/pjm.2002.202.363
Charles A. McCarthy, $c_{p}$, Israel J. Math. 5 (1967), 249–271. MR 225140, DOI 10.1007/BF02771613
Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149