Means of Hilbert Space Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Means of Hilbert Space Operators write by Fumio Hiai. This book was released on 2003-12-09. Means of Hilbert Space Operators available in PDF, EPUB and Kindle. The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.
Elements of Hilbert Spaces and Operator Theory
Elements of Hilbert Spaces and Operator Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of Hilbert Spaces and Operator Theory write by Harkrishan Lal Vasudeva. This book was released on 2017-03-27. Elements of Hilbert Spaces and Operator Theory available in PDF, EPUB and Kindle. The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.
Operators on Hilbert Space
Operators on Hilbert Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operators on Hilbert Space write by V. S. Sunder. This book was released on 2016-08-05. Operators on Hilbert Space available in PDF, EPUB and Kindle. The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.
Linear Operators in Hilbert Spaces
Linear Operators in Hilbert Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Operators in Hilbert Spaces write by Joachim Weidmann. This book was released on 2012-12-06. Linear Operators in Hilbert Spaces available in PDF, EPUB and Kindle. This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.
Numerical Ranges of Hilbert Space Operators
Numerical Ranges of Hilbert Space Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Ranges of Hilbert Space Operators write by Hwa-Long Gau. This book was released on 2021-08-05. Numerical Ranges of Hilbert Space Operators available in PDF, EPUB and Kindle. 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.
