More operator versions of the Schwarz inequality

Communications in Mathematical Physics

Volumn 215, Issue 2, 2000, Pages 239-244

  Bhatia, Rajendra ^a   Davis, Chandler ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349541     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000289     Document Type: Article

References (12)

1. [1] Ando, T.: Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra and its Applications 26, 203-241 (1979)
2. [2] Bhatia, R.: Matrix Analysis. Berlin-Heidelberg-New York: Springer, 1997
3. [3] Bhatia, R., Davis, Ch.: A better bound on the variance. American Mathematical Monthly 107, 353-356 (2000)
4. [4] Choi, M.-D.: Some assorted inequalities for positive linear maps on C*-algebras. Journal of Operator Theory 4, 271-285 (1980)
5. [5] Davis, Ch.: Various averaging operations onto subalgebras. Illinois J. Math. 3, 538-553 (1959)
6. [6] Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge: Cambridge University Press, 1985
7. [7] Kadison, R.V.: A generalized Schwarz inequality and algebraic invariants for C*-algebras. Ann. of Math. 56, 494-503 (1952)
8. [8] Lieb, E.H., Ruskai, M.B.: Some operator inequalities of the Schwarz type, Advances in Math. 12, 269-273 (1974)
9. [9] Marshall, A.W., Olkin, I.: Matrix versions of Cauchy and Kantorovich inequalities. Aequationes Math. 40, 89-93 (1990)
10. [10] Stinespring, W.F.: Positive functions on C*-algebras. Proc. Amer. Math. Soc. 6, 211-216 (1955)
11. [11] Wang, S.-G., Ip, W.-C.: A matrix version of the Wielandt inequality and its applications to statistics. Lin. Alg. Appl. 296, 171-181 (1999)
12. [12] Zhang, F.: Matrix inequalites in the Löwner ordering by means of block matrices and Schur complements. Preprint