An algebra of finitely additive measures
The algebra of finitely additive measures on a partially ordered semigroup
The calculus of operator functions and operator convexity
The paper is concerned with the Fréchet differentiability and operator convexity of the operator functions on sets of self-adjoint operators on finite-dimensional inner product spaces which are associated with real-valued functions of one or two variables. In Part I it is shown that if a real-valued function is L times continuously differentiable then the associated operator functions are L times Fréchet differentiable with continuous Fréchet derivatives. It is shown that the operator functions...
Convex and monotone operator functions
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.
Spaces of multipliers and their preduals for the order multiplication on [0, 1]
Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise and their preduals.
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