Strengthened convexity of positive operator monotone decreasing functions
نویسندگان
چکیده
منابع مشابه
Operator Monotone Functions, Positive Definite Kernels and Majorization
Let f(t) be a real continuous function on an interval, and consider the operator function f(X) defined for Hermitian operators X. We will show that if f(X) is increasing w.r.t. the operator order, then for F (t) = ∫ f(t)dt the operator function F (X) is convex. Let h(t) and g(t) be C1 functions defined on an interval I. Suppose h(t) is non-decreasing and g(t) is increasing. Then we will define ...
متن کاملModulus of convexity for operator convex functions
Most of the interesting examples deal with operators that are positive semi-definite. We shall follow the same convention in this paper. Operator convex functions are known to satisfy a number of interesting properties. An important discovery was made by Hansen and Pederson, who used Eq.1 in order to obtain an operator generalization of the Jensen inequality.[1] Recently, Effros provided an ele...
متن کاملOperator monotone functions of several variables
We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship between operator convexity and operator monotonicity for functions of one variable is extended also to functions of several variables.
متن کاملApplication of operator monotone functions in economics
Operator monotone functions play an important role in economics. We show that 2-monotonicity is equivalent to decreasing relative risk premium, a notion recently introduced in microeconomics. We also show that an operator monotone function is risk vulnerable, a notion introduced by Gollier and Pratt.
متن کاملOperator monotone functions and Löwner functions of several variables
We prove generalizations of Löwner’s results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuting self-adjoint n-by-n matrices. We prove a generalization to several variables of Nevanlinna’s theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth con...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2020
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-120579