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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

2013-09-14 Mathematics
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Release : 2013-09-14
Genre : Mathematics
Kind : eBook
Book Rating : 48X/5 ( reviews)

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Book Synopsis Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces by : Silvestru Sever Dragomir

Download or read book Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces written by Silvestru Sever Dragomir. This book was released on 2013-09-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces

2019-05-24 Mathematics
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Release : 2019-05-24
Genre : Mathematics
Kind : eBook
Book Rating : 59X/5 ( reviews)

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Book Synopsis Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces by : Silvestru Sever Dragomir

Download or read book Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces written by Silvestru Sever Dragomir. This book was released on 2019-05-24. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present results related to Kato's famous inequality for bounded linear operators on complex Hilbert spaces obtained by the author in a sequence of recent research papers. As Linear Operator Theory in Hilbert spaces plays a central role in contemporary mathematics, with numerous applications in fields including Partial Differential Equations, Approximation Theory, Optimization Theory, and Numerical Analysis, the volume is intended for use by both researchers in various fields and postgraduate students and scientists applying inequalities in their specific areas. For the sake of completeness, all the results presented are completely proved and the original references where they have been firstly obtained are mentioned.

Numerical Range

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 982/5 ( reviews)

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Book Synopsis Numerical Range by : Karl E. Gustafson

Download or read book Numerical Range written by Karl E. Gustafson. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.

Lectures on Numerical Radius Inequalities

2022-11-18 Mathematics
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Release : 2022-11-18
Genre : Mathematics
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Lectures on Numerical Radius Inequalities by : Pintu Bhunia

Download or read book Lectures on Numerical Radius Inequalities written by Pintu Bhunia. This book was released on 2022-11-18. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained advanced monograph on inequalities involving the numerical radius of bounded linear operators acting on complex Hilbert spaces. The study of numerical range and numerical radius has a long and distinguished history starting from the Rayleigh quotients used in the 19th century to nowadays applications in quantum information theory and quantum computing. This monograph is intended for use by both researchers and graduate students of mathematics, physics, and engineering who have a basic background in functional analysis and operator theory. The book provides several challenging problems and detailed arguments for the majority of the results. Each chapter ends with some notes about historical views or further extensions of the topics. It contains a bibliography of about 180 items, so it can be used as a reference book including many classical and modern numerical radius inequalities.

A Hilbert Space Problem Book

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 302/5 ( reviews)

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Book Synopsis A Hilbert Space Problem Book by : P.R. Halmos

Download or read book A Hilbert Space Problem Book written by P.R. Halmos. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

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