@article{ASNSP_1988_4_15_2_239_0, author = {Nussbaum, Roger D. and Cohen, Joel E.}, title = {The arithmetic-geometric mean and its generalizations for noncommuting linear operators}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {239--308}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 15}, number = {2}, year = {1988}, mrnumber = {1007399}, zbl = {0756.47018}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1988_4_15_2_239_0/} }
TY - JOUR AU - Nussbaum, Roger D. AU - Cohen, Joel E. TI - The arithmetic-geometric mean and its generalizations for noncommuting linear operators JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1988 SP - 239 EP - 308 VL - 15 IS - 2 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1988_4_15_2_239_0/ LA - en ID - ASNSP_1988_4_15_2_239_0 ER -
%0 Journal Article %A Nussbaum, Roger D. %A Cohen, Joel E. %T The arithmetic-geometric mean and its generalizations for noncommuting linear operators %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1988 %P 239-308 %V 15 %N 2 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1988_4_15_2_239_0/ %G en %F ASNSP_1988_4_15_2_239_0
Nussbaum, Roger D.; Cohen, Joel E. The arithmetic-geometric mean and its generalizations for noncommuting linear operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 2, pp. 239-308. http://archive.numdam.org/item/ASNSP_1988_4_15_2_239_0/
[1] Series and parallel addition of matrices, J. Math. Anal. Appl. 26 (1969), pp. 576-594. | MR | Zbl
- ,[2] Shorted operators II, SIAM J. Appl. Math. 28 (1975), pp. 60-71. | MR | Zbl
- ,[3] Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra and its Applications 27 (1979), pp. 203-241. | MR | Zbl
,[4] -, On the arithmetic-geometric-harmonic mean inequality for positive definite matrices, Linear Algebra and its Applications 52-53 (1983), pp. 31-37. | MR | Zbl
[5] Means of positive linear operators, Math. Ann. 246 (1980), pp. 205-244. | EuDML | MR | Zbl
- ,[6] Means and their iterations, in Proceedings of the Nineteenth Nordic Congress of Mathematicians, Reykjavik, 1984, pp. 191-212 (published by the Icelandic Math. Soc., 1985). | MR | Zbl
- - - ,[7] The analytic-functional calculus in commutative topological algebras, Pac. J. Math. 11 (1961), pp. 405-429. | MR | Zbl
,[8] Monotone and convex operator functions, Trans. Amer. Math. Soc. 79 (1955), pp. 58-71. | MR | Zbl
- ,[9] Gesammelte Werke, Herausgegeben von G. Hettner, Reimer. Berlin, 1888. | JFM
,[10] The arithmetic-geometric means and fast computation of elementary functions, SIAM Review 26 (1984), pp. 351-366. | MR | Zbl
- ,[11] A generalized arithmetic-geometric mean, Problem 83-12, SIAM Review 25 (1983), pp. 201.
- ,[12] Hidden symmetries of special functions, SIAM Review 12 (1970), pp. 332-345. | MR | Zbl
,[13] -, Algorithms involving arithmetic and geometric means, Amer. Math. Monthly 78 (1971), pp. 496-504. | MR | Zbl
[14] Arithmetic-geometric means of positive matrices, Math. Proc. Cambridge Phil. Soc. 101 (1987), pp. 209-219. | MR | Zbl
- ,[15] The arithmetic-geometric mean of Gauss, Enseignement Math. 30 (1984), Pl275-330. | MR | Zbl
,[16] Monotone Matrix Functions and Analytic Continuation, Springer-Verlag, New York, 1974. | MR | Zbl
,[17] Linear Operators, vol. 1, Interscience, New York, 1958. | Zbl
- ,[18] A generalization of the Gauss limit for iterated means, Advances in Math. 7 (1971), pp. 297-300. | MR | Zbl
- ,[19] Arithmetic-geometric means of operators, Math. Japonica 23 (1979), pp. 667-669. | MR | Zbl
,[20] Inequalities, 2nd ed., Cambridge University Press, 1959. | Zbl
- - ,[21] Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, New York, 1984. | Zbl
,[22] On the compounding of certain means, J. Math. Anal. Appl. 36 (1971), pp. 183-200. | MR | Zbl
,[23] Uber monotone Matrixfunktionen, Math. Zeit. 38 (1934), pp. 177-216. | JFM | MR | Zbl
- ,[24] Some classes of functions defined by difference or differential inequalities, Bull. Amer. Math. Soc. 56 (1950), pp. 308-319. | MR | Zbl
[25] Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979. | MR | Zbl
- ,[26] Iterated nonlinear maps and Hilbert's projective metric, Memoirs Amer. Math. Soc., no. 391 (1988). | Zbl
,[27] -, Iterated nonlinear maps and Hilbert's projective metric: a summary, in Dynamics of Infinite Dimensional Systems, edited by S.N. Chow and J.K. Hale, Springer Verlag, Heidelberg, 1987, pp. 231-249.
[28] -, Convexity and log convexity for the spectral radius, Linear Alg. and Appl. 73 (1986), pp. 59-122. | MR | Zbl
[29] A multivariable Tchebycheff inequality, Annals of Math. Stat. 29 (1958), pp. 226-234. | MR | Zbl
- ,[30] Iteration of power means and other related means, preprint, University of Lund, Sweden, 1984.
,[31] Functional calculus for sesquilinear forms, and the purification map, Rep. Math. Phys. 8 (1975), pp. 159-170. | MR | Zbl
- ,[32] Fast computation of matrix exponential and logarithm, Analysis (München) 5 (1985), pp. 163-173. | MR | Zbl
,[33] Introduction to Functional Analysis, Wiley, New York, 1958. | MR | Zbl
,[34] A multivariate generalization of Tchebychev's inequality, Quarterly J. of Math. Oxford, Series 2, 9 (1958), pp. 232-240. | MR | Zbl
,[35] Computation with Recurrence Relations, Pittman Advanced Publishing Program, Boston, 1984. | MR | Zbl
,[36] Functional Analysis, 6th ed., Springer-Verlag, New York, 1980.
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