Some Properties of Tensorial Perspective for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Sever Dragomir


Let H be a Hilbert space. Assume that f:[0,∞)→R is continuous and A, B>0. We define the tensorial perspective for the function f and the pair of operators (A,B) by


In this paper we show among others that, if f is differentiable convex, then


for A, B>0 and u>0. Moreover, if Sp(A)⊂I, Sp(B)⊂J and such that 0<γ≤(t/s)≤Γ for t∈I and s∈J, then

P_{f},_{⊗}(A,B) ≤[f(u)-f′(u)u](1⊗B)+f′(u)(A⊗1)

for u∈[γ,Γ].


  • There are currently no refbacks.