Inequalities for One Operator

  • Silvestru Sever Dragomir
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter we present with complete proofs some recent results obtained by the author concerning numerical radius and norm inequalities for a bounded linear operator on a complex Hilbert space. The techniques employed to prove the results are elementary. We also use some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke, Dragomir and Sándor as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Many references for the Kantorovich inequality that is extended here to larger classes of operators than positive operators are provided as well.


Numerical Radius Kantorovich Inequality Buzano Dragomir Complex Hilbert Space 
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Copyright information

© Silvestru Sever Dragomir 2013

Authors and Affiliations

  • Silvestru Sever Dragomir
    • 1
    • 2
  1. 1.College of Engineering and ScienceVictoria UniversityMelbourneAustralia
  2. 2.School of Computational and Applied MathematicsUniversity of the Withwatersrand BraamfonteinJohannesburgSouth Africa

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