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Numerical Ranges of Hilbert Space Operators

2021-08-05 Mathematics
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Release : 2021-08-05
Genre : Mathematics
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Book Rating : 606/5 ( reviews)

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Book Synopsis Numerical Ranges of Hilbert Space Operators by : Hwa-Long Gau

Download or read book Numerical Ranges of Hilbert Space Operators written by Hwa-Long Gau. This book was released on 2021-08-05. Available in PDF, EPUB and Kindle. Book excerpt: Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.

Numerical Ranges of Hilbert Space Operators

2021-07-31 Mathematics
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Release : 2021-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 066/5 ( reviews)

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Book Synopsis Numerical Ranges of Hilbert Space Operators by : Hwa-Long Gau

Download or read book Numerical Ranges of Hilbert Space Operators written by Hwa-Long Gau. This book was released on 2021-07-31. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Numerical Ranges and Commutation Properties of Hilbert Space Operators

1974
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Release : 1974
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Book Synopsis Numerical Ranges and Commutation Properties of Hilbert Space Operators by : Bruce Kent Richard

Download or read book Numerical Ranges and Commutation Properties of Hilbert Space Operators written by Bruce Kent Richard. This book was released on 1974. Available in PDF, EPUB and Kindle. Book excerpt:

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
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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.

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