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ArticleOriginal scientific text

Title

Convex and monotone operator functions

Authors 1, 2

Affiliations

  1. Department of Applied Mathematics, Regional Engineering College, Jalandhar, Punjab, India
  2. Department of Mathematics, Panjab University, Chandigarh, India

Abstract

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.

Keywords

ENG
operator monotone function, operator convex function

Bibliography

  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.
Annales Polonici Mathematici
1995/62/1
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Pages:
1-11
Main language of publication
English
Received
1993-05-20
Published
1995
Exact and natural sciences