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## The calculus of operator functions and operator convexity

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 390 wydano: 2000
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Abstrakty
EN
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 corresponding to a real-valued function f can be expressed algebraically in terms of its first Fréchet derivatives. There are then the natural differential conditions for operator monotonicity and convexity and the latter is used in Part II which is concerned with operator convex functions of two variables. The set 𝓞 𝓒₂ of operator convex functions on (-1,1)² is a convex cone. A three-parameter family of faces F(α,β,e), of dimension 3 (the trivial case), 4, 6, 7 or 8, of 𝓞 𝓒₂ is identified and investigated.
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Miejsce publikacji
Warszawa
Seria
Rozprawy Matematyczne tom/nr w serii: 390
Liczba stron
48
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Opis fizyczny
Daty
wydano
2000
Twórcy
autor
• Department of Mathematics, Panjab University, Chandigarh, India
autor
• Department of Mathematics, Panjab University, Chandigarh, India
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Języki publikacji
 EN
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