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SpringerBriefs in Mathematics

Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

Authors: Dragomir, Silvestru Sever

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  • Centered on numerical radius inequalities for bounded linear operators on complex
  • Hilbert spaces for the case of one and two operators Classical inequalities due to Berger, Holbrook, Fong and Holbrook and Bouldin are given
  • Numerous references for the Kantorovich inequality that is extended to larger classes of operators than positive operators are provided​
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eBook 42,79 €
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  • ISBN 978-3-319-01448-7
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Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-01447-0
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About this book

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.

Reviews

From the book reviews:

“The aim of this book is to provide several inequalities, mainly obtained by the author, concerning the numerical radius of linear operators. … The book is easy to read and should be accessible to undergraduates taking a course in operator theory.” (Cătălin Badea, zbMATH, Vol. 1302, 2015)

“The author discusses various numerical radius inequalities for bounded linear operators in complex Hilbert spaces. … The book is appropriate for researchers and graduate students in the area of linear operator theory in Hilbert spaces, or as a reference book for researchers in different mathematical disciplines using inequalities involving the numerical radius of a linear operator. … the book is well written and provides a good summary of the author’s recent results.” (Tsvetanka Sendova, Mathematical Reviews, June, 2014)


Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-319-01448-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-01447-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Silvestru Sever Dragomir
eBook ISBN
978-3-319-01448-7
DOI
10.1007/978-3-319-01448-7
Softcover ISBN
978-3-319-01447-0
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 120
Topics