Paper Title:

Some Operator Order Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Author(s):

S. S. Dragomir^1,2 and Charles E. M. Pearce³

¹Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

²School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au 
URL: http://rgmia.org/dragomir

³School of Mathematical Sciences,
The University of Adelaide,
Adelaide,
Australia
 

Abstract:

Various bounds in the operator order for the following operator transform

where A is a selfadjoint operator in the Hilbert space H with the spectrum Sp( A) ⊆ [ m,M] and f:[m,M] ->  C is a continuous function on [m,M]  are given. Applications for the power and logarithmic functions are provided as well.

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