Convex and monotone operator functions

• Autorzy: Jaspal Singh Aujla , H. L. Vasudeva
• Języki publikacji: EN

Abstrakty

EN

The purpose of this note is to provide characterizations of operator convexity and give an alternative proof of a two-dimensional analogue of a theorem of Löwner concerning operator monotonicity.

Słowa kluczowe

EN

operator monotone function; operator convex function

Kategorie tematyczne

• 26B25: Convexity, generalizations
• 15A45: Miscellaneous inequalities involving matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 1
• Strony: 1-11

Daty

wydano

1995

otrzymano

1993-05-20

Twórcy

autor

Jaspal Singh Aujla

• Department of Applied Mathematics, Regional Engineering College, Jalandhar, Punjab, India

autor

H. L. Vasudeva

• Department of Mathematics, Panjab University, Chandigarh, India

Bibliografia

• [1] T. Ando, Topics on Operator Inequalities, lecture notes (mimeographed), Hokkaido University, Sapporo, 1978.
• [2] C. Davis, Notions generalizing convexity for functions defined on spaces of matrices, in: Proc. Sympos. Pure Math. 7, Amer. Math. Soc., 1963, 187-201.
• [3] W. F. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Springer, Heidelberg, 1974.
• [4] F. Hansen and G. K. Pedersen, Jensen's inequality for operators and Löwner's theorem, Math. Ann. 258 (1982), 229-241.
• [5] A. Korányi, On a class of analytic functions of several variables, Trans. Amer. Math. Soc. 101 (1961), 521-554.
• [6] F. Kraus, Über konvexe Matrixfunktionen, Math. Z. 41 (1936), 18-41.
• [7] C. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216.
• [8] A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973.
• [9] H. Vasudeva, On monotone matrix functions of two variables, Trans. Amer. Math. Soc. 176 (1973), 303-318.