# 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

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topJaspal 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

top- [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. Zbl0196.30303
- [3] W. F. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Springer, Heidelberg, 1974. Zbl0278.30004
- [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] A. Korányi, On a class of analytic functions of several variables, Trans. Amer. Math. Soc. 101 (1961), 521-554. Zbl0111.11501
- [6] F. Kraus, Über konvexe Matrixfunktionen, Math. Z. 41 (1936), 18-41. Zbl0013.39701
- [7] C. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216. Zbl0008.11301
- [8] A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973. Zbl0271.26009
- [9] H. Vasudeva, On monotone matrix functions of two variables, Trans. Amer. Math. Soc. 176 (1973), 303-318. Zbl0261.26009

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