6 edition of **Linear operators in spaces with an indefinite metric** found in the catalog.

- 102 Want to read
- 20 Currently reading

Published
**1989** by Wiley in Chichester [England], New York .

Written in English

- Linear operators.

**Edition Notes**

Statement | T.Ya. Azizov, I.S. Iokhvidov ; translated by E.R. Dawson. |

Series | Pure and applied mathematics, Pure and applied mathematics (John Wiley & Sons : unnumbered) |

Contributions | Iokhvidov, I. S. |

Classifications | |
---|---|

LC Classifications | QA329.2 .A9913 1989 |

The Physical Object | |

Pagination | xi, 304 p. : |

Number of Pages | 304 |

ID Numbers | |

Open Library | OL2195168M |

ISBN 10 | 0471921297 |

LC Control Number | 89014655 |

n-dimensional spaces with indefinite scalar products defined by invertible Hermitian operators Hi and Hz respectively. These spaces are called iso- metric if there exists a linear operator U: Cy -+ Ci that preserves the indefinite scalar product, i.e., such that [ux, uY]H, = 1x7 Y]Hl vx,y E cy. Continuous Linear Operators Between Banach Spaces. Normed Linear Spaces. Linear Operators. Compactness Lost: Infinite Dimensional Normed Linear Spaces. The Open Mapping and Closed Graph Theorems. The Uniform Boundedness Principle Duality for Normed Linear Spaces. Linear Functionals, Bounded Linear Functionals. The parallel to the theory of symmetric operators in an indefinite metric space is natural and necessary; both symmetries have the form, with a conjugate-linear involution in the first case, and a unitary involution in the second. The geometry of spaces with an indefinite metric Linear spaces with an Hermitian form Krein spaces (axiomatics) §3 Canonical projectors P± and canonical symmetry J §4 Semi-definite and definite lineals and subspaces in a Krein 1 §2 14 §6 §7 24 of the classes h± Decomposability of lineals and subspaces of a .

Remarks on numerical ranges of operators in spaces with an indefinite metric (with L. Rodman), Proc. of Amer. Math. Soc. (), pp. {} Estimating the Extreme Singular Values of Matrices, (with C. Pohanka*), Mathematical Inequalities and Applications 1 (),

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Get this from a library. Linear operators in spaces with an indefinite metric. [T I︠A︡ Azizov; I S Iokhvidov] -- An introduction to the geometry of spaces, this research monograph develops the foundations of the theory of linear operators in these spaces and examines the theory of invariant subspaces, spectral.

A monograph on the fundamentals of the theory of linear operators in spaces with an indefinite metric. Introduces the geometry of spaces with indefinite metric, and the central topics of operator theory, and explores variations on the by: The geometry of spaces with an indefinite metric; fundamental classes of operators in spaces with an indefinite metric; invariant semi-definite subspaces; spectral topics and some applications; theory of extensions of isometric and symmetric operators in spaces with an indefinite metric.

Series Title: A Wiley Interscience publication. Linear Operators in Spaces with an Indefinite Metric (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) by Azizov, T. Ya., Iokhvidov, I.

and a great selection of related books, art and collectibles available now at Inner products and the metric operator. Consider a complex vector space equipped with an indefinite hermitian form ⋅, ⋅.In the theory of Krein spaces it is common to call such an hermitian form an indefinite inner following subsets are defined in terms of the square norm induced by the indefinite inner product: = {∈: =} ("neutral").

Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are presented.

This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th book begins with his biography and list of publications.

It contains a selection of research. Remarks on numerical ranges of operators in spaces with an indefinite metric Article (PDF Available) in Proceedings of the American Mathematical Society () May with Contractive linear relations in Hilbert spaces are (graphs of) operators, but in spaces with an indefinite metric this is not always true.

The presence of a multivalued part gives difficulties in the characterization of maximal contractive linear relations and in the proof of the existence of invariant : T. Ya Azizov, A. Dijksma. Keywords: Linear operators, spaces with indefinite metric, differential equa tions, operator valued analytic functions, interpolation prob lems.

Mathematics Subject Classification:,This volume is dedicated to Professor Heinz Langer to honor him for. Request PDF | Representations of Nilpotent Groups on Spaces with Indefinite Metric | The paper studies the structure of J-unitary representations of connected nilpotent groups on \(\Pi _{k.

The geometry of spaces with an indefinite metric-- fundamental classes of operators in spaces with an indefinite metric-- invariant semi-definite subspaces-- spectral topics and some applications-- theory of extensions of isometric and symmetric operators in spaces with an indefinite metric.

(source: Nielsen Book Data) This research monograph. Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are : Birkhäuser Basel.

In linear algebra, an inner product space is a vector space with an additional structure called an inner additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.

Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the angle between two vectors. Early work of Phillips, Krein and Naimark on operators in such spaces is discussed e.g. in Helton, Unitary Operators on a Space with an Indefinite Inner Product, a book treatment is Azizov-Iokhvidov, Linear operators in spaces with an indefinite metric.

From Mathematics Subject Classification includes 47B Operators on spaces with an. This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations.

It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. They reflect most of the topics dealt with by the modern operator theory, including recent advances in dual operator algebras and the fnvariant subspace problem, operators in indefinite metric spaces, hyponormal, quasi triangular and decomposable operators, various problems in C*- and W*-algebras and so : Parameters Associated with Normed Linear Spaces and Inner Product Structures.

Linear Operators on Spaces with an Indefinite Inner Product. Some Classes of Spaces with an Indefinite Metric. Modules with an Indefinite Inner Product. Next is an introduction to linear spaces, with coverage of linear operators, eigenvalue and the stability problem of linear operators, and matrices with special properties.

Material on binary product spaces features self-adjoint operators in a space of indefinite metric, binary product spaces with a positive definite metric, properties of the Author: Per-Olov Löwdin.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

Next we recall some definitions and results concerning linear operators acting between indefinite scalar product spaces. We shall frequently identify operators with matrices in the usual way. Let Hp respectively H2, be a Hermitean invertible m x m, respectively n x n, matrix.

The H1H2-adjoint A[*] of an m x n matrix A is defined by the identity. Author of Lectures on invariant subspaces, Harmonic analysis, Sous-espaces invariants, Linear algebra, Operators in Indefinite Metric Spaces, Scattering Theory, and Other Topics (Operator Theory, Advances and Applications), Honors Calculus.

Next is an introduction to linear spaces, with coverage of linear operators, eigenvalue and the stability problem of linear operators, and matrices with special properties. Material on binary product spaces features self-adjoint operators in a space of indefinite metric, binary product spaces with a positive definite metric, properties of the.

Enjoy millions of the latest Android apps, games, music, movies, TV, books, magazines & more. Anytime, anywhere, across your devices. LINEAR OPERATORS AND FUNCTIONALS. L.V. KANTOROVICH, G.P. AKILOV, in Functional Analysis (Second Edition) Let A be a self-adjoint operator in the space the paper [15] the problem on the existence of invariant subspaces stays in the center of the.

Linear Operators in Function Spaces: 12th International Conference on Operator Theory Timi?oara (Romania) June 6 16, Operator Algebras and Group Representations (Monograph & Studies in Mathematics) Operators in Indefinite Metric Spaces, Scattering Theory and Other Topics: 10th Intern.

A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis.

As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and. This paper resolves a number of problems in the perturbation theory of linear operators, linked with the year-old conjecure of M. Kreĭn. In particular, we prove that every Lipschitz function is operator-Lipschitz in the Schatten–von Neumann ideals S α, 1 Cited by: This is a list of all mathematics courses.

For more information, see Mathematics. MATH Basic Algebra I 3 s.h. Percents, ratio and proportion, algebraic expressions and operations, simple products, linear and quadratic equations, simultaneous equations, exponents and radicals; emphasis on verbal problems.

MATH Basic Geometry 3 s.h. Continuous Linear Operators Between Banach Spaces. Normed Linear Spaces. Linear Operators. Compactness Lost: Infinite Dimensional Normed Linear Spaces. The Open Mapping and Closed Graph Theorems.

The Uniform Boundedness Principle. Duality for Normed Linear Spaces. Linear Functionals, Bounded Linear Functionals /5(3). After the book "Basic Operator Theory" by Gohberg-Goldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications.

The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics. Non-Archimedean Inner Product Spaces.- Nonstandard Inner Product Spaces.- Intuitionistic Complete Inner Product Spaces.- Constructive Inner Product Spaces.- 16/Indefinite Inner Product Structures.- Introduction.- Indefinite Inner Product Linear Spaces.- Orthogonality and Orthogonal Decomposition.- Linear.

Another important area of linear algebra, the geometry of indefinite inner product spaces and the spectral theory of operators on these spaces, has its origin in Dirac's work on quantum theory. The mathematical foundation was laid by Pontrjagin, M.

Krein and his by: 1. Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.

The publication first offers information on algebraic theory of vector spaces and introduction to functional Edition: 1. Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization.

Keywords: Differential operators, integral operators, singularities, spectral problems, factorization, dilations, approximation of operators, spaces with indefinite metric.

Mathematics Subject Classification:andThis two volume book represents the. A bridge between operator theory and mathematical biology ; Measures on effects and on projections in spaces with indefinite metric ; Concentration behavior of solutions to a chemotaxis system ; The solution of linear semidefinite ill-posed.

Contributions to Operator Theory in Spaces with an Indefinite Metric, () The boundary of the numerical range of matrix polynomials. Linear Algebra and its ApplicationsCited by: () Singular numbers of contractions in spaces with an indefinite metric and Yamamoto's theorem.

Linear Algebra and its ApplicationsPaul Binding and Hans by: Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space.

It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP-space).Cited by: 9. We have been very encouraged by the reactions of students and teachers using our book over the past ten years and so this is a complete retype in TEX, with corrections of known errors and the addition of a supplementary bibliography.

Thanks are due to the Springer staff in Heidelberg for their enthusiastic sup port and to the typist, Armin Kollner for the excellence of the final result.MATH Introduction to Hilbert Spaces. 3 Credit Hours. Geometry, convergence, and structure of linear operators in infinite dimensional spaces.

Applications to science and engineering, including integral equations and ordinary partial differential equations.This work aims to give a systematic presentation of methods used in the spectral theory of non-selfadjoint, generally unbounded, operators.

Subjects treated include: the wide class of both selfadjoint and non-selfadjoint extensions of Hermitian operators; characteristic functions of a regular extension; the construction of some operator models for different classes of non-selfa.