Add to ORKGWe prove that a real-valued function f defined on an interval S in R is matrix convex if and only if for any natural k, for all families of positive operators { Ai }i = 1 k in a finite-dimensional Hilbert space, such that ∑i = 1 k Ai = 1, and arbitrary numbers xi ∈ S, the inequality{A formula is presented}holds true. © 2006 Elsevier Inc. All rights reserved
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
AbstractLet I, J be intervals such that 0 ∈ I ∩ J. Let Mm be the algebra of all m ×m complex matrice...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
AbstractWe prove that a real-valued function f defined on an interval S in R is matrix convex if and...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
AbstractWe prove that a real-valued function f defined on an interval S in R is matrix convex if and...
Abstract. We give a survey of various operator inequalities associated with Jensen’s inequality and ...
AbstractSeveral basic results of convexity theory are generalized to the “quantized” matrix convex s...
AbstractLet Sn be the set of all n×n real symmetric matrices. We give a complete characterization of...
AbstractJensen's operator inequality characterizes operator convex functions of two variables (F. Ha...
Abstract A real-valued continuous function on an interval gives rise to a map via functional c...
A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X!...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
AbstractLet I, J be intervals such that 0 ∈ I ∩ J. Let Mm be the algebra of all m ×m complex matrice...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
AbstractWe prove that a real-valued function f defined on an interval S in R is matrix convex if and...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
AbstractWe prove that a real-valued function f defined on an interval S in R is matrix convex if and...
Abstract. We give a survey of various operator inequalities associated with Jensen’s inequality and ...
AbstractSeveral basic results of convexity theory are generalized to the “quantized” matrix convex s...
AbstractLet Sn be the set of all n×n real symmetric matrices. We give a complete characterization of...
AbstractJensen's operator inequality characterizes operator convex functions of two variables (F. Ha...
Abstract A real-valued continuous function on an interval gives rise to a map via functional c...
A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X!...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
We prove that a real function is operator monotone (operator convex) if the corresponding monotonici...
AbstractLet I, J be intervals such that 0 ∈ I ∩ J. Let Mm be the algebra of all m ×m complex matrice...