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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

  • Silvestru Sever Dragomir

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Silvestru Sever Dragomir
    Pages 1-7
  3. Silvestru Sever Dragomir
    Pages 9-60
  4. Silvestru Sever Dragomir
    Pages 61-120

About this book

Introduction

Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents  recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.

Keywords

Euclidean operator radius Grüss type inequalities Linear operator theory complex Hilbert spaces numerical radius inequalities

Authors and affiliations

  • Silvestru Sever Dragomir
    • 1
  1. 1.College of Engineering & Science; School of Computational and Applied MathematicsVictoria University, Melbourne, Australia, and University of the WithwatersrandBraamfonteinSouth Africa

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01448-7
  • Copyright Information Silvestru Sever Dragomir 2013
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-01447-0
  • Online ISBN 978-3-319-01448-7
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site