The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

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


S. S. Dragomir1,2 and Charles E. M. Pearce3

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

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

3School of Mathematical Sciences,
The University of Adelaide,


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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