Hokkaido Mathematical Journal

A normal family of operator monotone functions

Mohammad Sal MOSLEHIAN, Hamed NAJAFI, and Mitsuru UCHIYAMA

Full-text: Open access

Abstract

We show that the family of all operator monotone functions f on (-1,1) such that f(0) = 0 and f′(0) = 1 is a normal family and investigate some properties of odd operator monotone functions. We also characterize the odd operator monotone functions and even operator convex functions on (-1,1). As a consequence, we show that if f is an odd operator monotone function on (-1,1), then f is concave on (-1,0) and convex on (0,1).

Article information

Source
Hokkaido Math. J., Volume 42, Number 3 (2013), 417-423.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1384273390

Digital Object Identifier
doi:10.14492/hokmj/1384273390

Mathematical Reviews number (MathSciNet)
MR3137393

Zentralblatt MATH identifier
1279.47032

Subjects
Primary: 47A63: Operator inequalities 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)

Keywords
Operator monotone function operator convex function normal family integral representation

Citation

MOSLEHIAN, Mohammad Sal; NAJAFI, Hamed; UCHIYAMA, Mitsuru. A normal family of operator monotone functions. Hokkaido Math. J. 42 (2013), no. 3, 417--423. doi:10.14492/hokmj/1384273390. https://projecteuclid.org/euclid.hokmj/1384273390


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