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  • References

    C. Akemann, J. Anderson and G. Pedersen, Triangle inequalities in oper- ator algebras, Linear and Multilinear Algebra, 11(1982) 167-178.

    A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge University Press, 1993.

    A.R. Amir-Moez, Extreme Properties of Linear Transformations and Ge- ometry in Unitary Spaces, Texas Tech. University, 1968.

    W.N. Anderson and G.E. Trapp, A class of monotone operator functions related to electrical network theory, Linear Algebra Appl., 15(1975) 53- 67.

    T. Ando, Topics on operator inequalities, Hokkaido University, Sapporo, 1978.

    T. Ando, Concavity of certain maps on positive definite matrices and appli- cations to Hadamard products, Linear Algebra Appl., 26(1979) 203-24l.

    T. Ando, Inequalities for permanents, Hokkaido Math. J., 10(1981) 18-36.

    T. Ando, Comparison of norms Illf(A)- f(B)1I1 and IIlf(IA-BI)III, Math. Z., 197(1988) 403-409.

    T. Ando, Majorization, doubly stochastic matrices and comparison of eigen- values, Linear Algebra Appl., 118(1989) 163-248.

    T. Ando, Matrix Young inequalities, Operator Theory: Advances and Ap- plications, 75(1995) 33-38.

    T. Ando, Bounds for the antidistance, J. Convex Analysis, 2(1996) 1-3.

    T. Ando and R. Bhatia, Eigenvalue inequalities associated with the Carte- sian decomposition, Linear and Multilinear Algebra, 22 (1987) 133-147.

  • 326 References

    T. Ando and F. Hiai, Log majorization and complementary Golden- Thomp- son type inequalities, Linear Algebra Appl., 197/198(1994) 113-13l.

    H. Araki, On an inequality of Lieb and Thirring, Letters in Math. Phys., 19(1990) 167-170.

    H. Araki and S. Yamagami, An inequality for the Hilbert-Schmidt norm, Commun. Math. Phys., 81(1981) 89-98.

    N. Aronszajn, Rayleigh-Ritz and A. Weinstein methods for approximation of eigenvalues. 1. Operators in a Hilbert space, Proc. Nat. Acad. Sci. U.S.A., 34(1948) 474-480.

    W.B. Arveson, Notes on extensions of CO-algebras, Duke Math. J., 44 (1977) 329-355.

    J.S. Aujla and H.L. Vasudeva, Convex and monotone operator functions, Ann. Polonici Math., 62(1995) 1-11.

    F.L. Bauer and C.T. Fike, Norms and exclusion theorems, Numer. Math. 2(1960) 137-141.

    H. Baumgiirtel, Analytic Perturbation Theory for Matrices and Operators, Birkhiiuser, 1984.

    N. Bebiano, New developments on the Marcus-Oliviera conjecture, Linear Algebra Appl., 197/198(1994) 793-802.

    G.R. Belitskii and Y.I. Lyubich, Matrix Norms and Their Applications, Birkhiiuser, 1988.

    J. Bendat and S. Sherman, Monotone and convex operator functions, Trans. Amer. Math. Soc., 79(1955) 58-71.

    F. Berezin and LM. Gel'fand, Some remarks on the theory of spherical functions on symmetric Riemannian manifolds, Trudi Moscow Math. Ob., 5(1956) 311-351.

    R. Bhatia, On the rate of change of spectra of operators II, Linear Algebra Appl., 36(1981) 25-32.

    R. Bhatia, Analysis of spectral variation and some inequalities, Trans. Amer. Math. Soc., 272(1982) 323-332.

    R, Bhatia, Some inequalities for norm ideals, Commun. Math. Phys., 111(1987) 33-39.

    R. Bhatia, Perturbation Bounds for Matrix Eigenvalues, Longman, 1987.

    R. Bhatia, Perturbation inequalities for the absolute value map in norm ideals of operators, J. Operator Theory, 19(1988) 129-136.

    R. Bhatia, On residual bounds for eigenvalues, Indian J. Pure Appl. Math., 23(1992) 865-866.

    R. Bhatia, A simple proof of an operator inequality of focic and Kittaneh, J. Operator Theory, 31 (1994) 21-22.

    R. Bhatia, Matrix factorizations and their perturbations, Linear Algebra Appl., 197/198(1994) 245-276.

  • References 327

    R. Bhatia, First and second order perturbation bounds for the opemtor absolute value, Linear Algebra Appl., 208/209(1994) 367-376.

    R. Bhatia, Perturbation bounds for the opemtor absolute value, Linear Al- gebra Appl., 226(1995) 639-645.

    R. Bhatia and C. Davis, A bound for the spectml variation of a unitary opemtor, Linear and Multilinear Algebra, 15(1984) 71-76.

    R. Bhatia and C. Davis, Concavity of certain functions of matrices, Linear and Multilinear Algebra, 17(1985) 155-164.

    R. Bhatia and C. Davis, More matrix forms of the arithmetic-geometric mean inequality, SIAM J. Matrix Analysis, 14(1993) 132-136.

    R. Bhatia and C. Davis, Relations of linking and duality between sym- metric gauge functions, Operator Theory: Advances and Applications, 73(1994) 127-137.

    R. Bhatia and C. Davis, A Cauchy-Schwarz inequality for opemtors with applications, Linear Algebra Appl., 223(1995) 119-129.

    R. Bhatia, C. Davis, and F. Kittaneh, Some inequalities for commutators and an application to spectml variation, Aequationes Math., 41(1991) 70-78.

    R. Bhatia, C. Davis and A. McIntosh, Perturbation of spectml sub- spaces and solution of linear opemtor equations, Linear Algebra Appl., 52/53(1983) 45-67.

    R. Bhatia a~d L. Elsner, On the variation of permanents, Linear and Mul- tilinear Algebra, 27(1990) 105-110.

    R. Bhatia and L. Elsner, Symmetries and variation of spectm, Canadian J. Math., 44(1992) 1155-1166

    R. Bhatia and L. Elsner, The q-binomial theorem and spectml symmetry, Indag. Math., N.S., 4(1993) 11-16.

    R. Bhatia, L. Elsner, and G. Krause, Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix, Linear Algebra Appl., 142(1990) 195-209.

    R. Bhatia, L. Elsner, and G. Krause, Spectml variation bounds for diago- nalisable matrices, Preprint 94-098, SFB 343, University of Bielefeld, Aequationes Math., to appear.

    R. Bhatia and S. Friedland, Variation of Gmssmann powers and spectra, Linear Algebra Appl., 40(1981) 1-18.

    R. Bhatia and J.A.R. Holbrook, Short normal paths and spectml variation, Proc. Amer. Math. Soc., 94(1985) 377-382.

    R. Bhatia and J.A.R. Holbrook, Unitary invariance and spectml varia.tion, Linear Algebra Appl., 95(1987) 43-68.

    R. Bhatia and J.A.R. Holbrook, A softer, stronger Lidskii theorem, Proc. Indian Acad. Sci. (Math. Sci.), 99(1989) 75-83.

  • 328 References

    R. Bhatia, R. Horn, and F. Kittaneh, Normal approximants to binormal opemtors, Linear Algebra Appl., 147(1991) 169-179.

    R. Bhatia and F. Kittaneh, On some perturbation inequalities for opemtors, Linear Algebra Appl., 106(1988) 271-279.

    R. Bhatia and F. Kittaneh, On the singular values of a product of opemtors, SIAM J. Matrix Analysis, 11(1990) 272-277.

    R. Bhatia and F. Kittaneh, Some inequalities for norms of commutators, SIAM J. Matrix Analysis, 18(1997) to appear.

    R. Bhatia, F. Kittaneh and R.-C. Li, Some inequalities for commutators and an application to spectml variation II, Linear and Multilinear Algebra, to appear.

    R. Bhatia and K.K. Mukherjea, On the mte of change of spectm of opem- tors, Linear Algebra Appl., 27(1979) 147-157.

    R. Bhatia and K.K. Mukherjea, The space of unordered types of complex numbers, Linear Algebra Appl., 52/53(1983) 765-768.

    R. Bhatia and K. Mukherjea, Variation of the unitary part of a matrix, SIAM J. Matrix Analysis, 15(1994) 1007-1014.

    R. Bhatia and P. Rosenthal, How and why to solve the equation AX - X B = Y, Bull. London Math. Soc., 29(1997) to appear.

    R. Bhatia and K.B. Sinha, Variation of real powers of positive opemtors, Indiana Univ. Math. J., 43(1994) 913-925.

    M.Sh. Birman, L.S. Koplienko, and M.Z. Solomyak, Estimates of the spec- trum of the difference between fractional powers of self-adjoint opem- tors, Izvestiya Vysshikh Uchebnykh Zavedenni. Mat, 19(1975) 3-10.

    M. Sh. Birman and M.Z. Solomyak Double Stieltjes opemtor integmls, En- glish translation, in Topics in Mathematical Physics, Volume 1, Con- sultant Bureau, New York, 1967.

    A. Bjorck and G.H. Golub, Numerical methods for computing angles be- tween linear subspaces, Math. Compo 27(1973) 579-594.

    R. Bouldin, Best approximation of a normal opemtor in the Schatten p- norm, Proc. Amer. Math. Soc., 80(1980) 277-282.

    A.L. Cauchy, Sur l'equation a l'aide de laquelle on determine les inegalites seculaires des mouvements des planetes,1829, Oeuvres Completes, (lInd Serie) Volume 9, Gauthier-Villars.

    F. Chatelin, Spectral Approximation of Linear Operators, Academic Press 1983.

    M.D. Choi, Almost commuting matrices need not be neaTly commuting, Proc. Amer. Math. Soc. 102(1988) 529-533.

    J.E. Cohen, Inequalities for matrix exponentials, Linear Algebra Appl., 111(1988) 25-28.

  • References 329

    J.E. Cohen, S. Friedland, T. Kato, and F.P. Kelly, Eigenvalue inequalities for products of matrix exponentials, Linear Algebra Appl., 45(1982) 55-95.

    A. Connes and E. Stl/lrmer, Entropy for automorphisms of I h von Neu- mann algebras, Acta Math., 134(1975) 289-306.

    H.O. Cordes, Spectral Theory of Linear Differential Operators and Com- parison Algebras, Cambridge University Press, 1987.

    R. Courant, Uber die Eigenwerte bei den Differentialgleichungen der math- ematischen Physik, Math. Z., 7(1920) 1-57.

    R. Courant and D. Hilbert, Methods of Mathematical Physics, Wiley, 1953.

    Ju. L. Daleckii and S.G. Krein, Formulas of differentiation according to a parameter of functions of Hermitian operators, Dokl. Akad. Nauk SSSR, 76(1951) 13-16.

    E.B. Davies, Lipschitz continuity of functions of operators in the Schatten classes, J. London Math. Soc., 37(1988)148~157.

    C. Davis, Separation of two linear subspaces, Acta Sci. Math. (Szeged), 19(1958) 172-187.

    C. Davis, Notions generalizin