Another operator version of generalized Bernoulli’s inequality

Abstract

In a recent paper by Pal, Singh and Aujla, a general version of second-order Bernoulli’s inequality is proved. Motivated from this, we shall prove yet another generalized form of this inequality. As an application the significant generalized difference operator mean inequalities, equalities and their eigenvalue inequalities will be proved for two positive invertible operators and on a seperable Hilbert space under the condition that is compact.

Keywords:

• Bernoulli’s inequality
• positive operator
• operator mean
• Heinz inequality

AMS Subject Classifications:

• Primary 47A63
• Secondary 47A10
• 47A30
• 47A64
• 47B07
• 47B15

Acknowledgements

The first author would like to sincerely thank the Council of Scientific & Industrial Research, Human Resource Development Group, India for grant of Senior Research Fellowship vide letter no. 09/797(0009)/2012-EMR-I.