Convex and monotone operator functions

Jaspal Singh Aujla; H. L. Vasudeva

Annales Polonici Mathematici (1995)

  • Volume: 62, Issue: 1, page 1-11
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jaspal Singh Aujla, and H. L. Vasudeva. "Convex and monotone operator functions." Annales Polonici Mathematici 62.1 (1995): 1-11. <http://eudml.org/doc/262355>.

@article{JaspalSinghAujla1995,
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.},
author = {Jaspal Singh Aujla, H. L. Vasudeva},
journal = {Annales Polonici Mathematici},
keywords = {operator monotone function; operator convex function; convex operator function; monotone operator function},
language = {eng},
number = {1},
pages = {1-11},
title = {Convex and monotone operator functions},
url = {http://eudml.org/doc/262355},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Jaspal Singh Aujla
AU - H. L. Vasudeva
TI - Convex and monotone operator functions
JO - Annales Polonici Mathematici
PY - 1995
VL - 62
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - operator monotone function; operator convex function; convex operator function; monotone operator function
UR - http://eudml.org/doc/262355
ER -

References

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  1. [1] T. Ando, Topics on Operator Inequalities, lecture notes (mimeographed), Hokkaido University, Sapporo, 1978. 
  2. [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. Zbl0196.30303
  3. [3] W. F. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Springer, Heidelberg, 1974. Zbl0278.30004
  4. [4] F. Hansen and G. K. Pedersen, Jensen's inequality for operators and Löwner's theorem, Math. Ann. 258 (1982), 229-241. Zbl0473.47011
  5. [5] A. Korányi, On a class of analytic functions of several variables, Trans. Amer. Math. Soc. 101 (1961), 521-554. Zbl0111.11501
  6. [6] F. Kraus, Über konvexe Matrixfunktionen, Math. Z. 41 (1936), 18-41. Zbl0013.39701
  7. [7] C. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216. Zbl0008.11301
  8. [8] A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973. Zbl0271.26009
  9. [9] H. Vasudeva, On monotone matrix functions of two variables, Trans. Amer. Math. Soc. 176 (1973), 303-318. Zbl0261.26009

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