3 edition of **Characterizations of inner product spaces** found in the catalog.

Characterizations of inner product spaces

Dan Amir

- 30 Want to read
- 18 Currently reading

Published
**1986**
by Birkhäuser Verlag in Basel, Boston
.

Written in English

- Inner product spaces.

**Edition Notes**

Statement | Dan Amir. |

Series | Operator theory, advances and applications -- v. 20., Operator theory, advances and applications -- v. 20. |

Classifications | |
---|---|

LC Classifications | QA322.4 .A46 1986 |

The Physical Object | |

Pagination | 200 p. : |

Number of Pages | 200 |

ID Numbers | |

Open Library | OL20200179M |

ISBN 10 | 0817617744 |

LC Control Number | 86018807 |

The purpose of this book is to give systematic and comprehensive presentation of theory of n-metric spaces, linear n-normed spaces and n-inner product spaces (and so 2-metric spaces, linear 2-normed spaces and 2-linner product spaces n=2). Since and , S. Gahler published two papers entitled "2-metrische Raume und ihr topologische Strukhur" and "Lineare 2-normierte Raume", a number of. Norm derivatives: Definition and basic properties. Orthogonality relations based on norm derivatives. ρ′ ±-orthogonal transformations. On the equivalence of two norm derivatives. Norm derivatives and projections in normed linear spaces. Norm derivatives and Lagrange's identity in normed linear spaces. On some extensions of the norm derivatives.

Yes, there are many (simple) characterizations of when a normed space is an inner product space. Here are two book references, one with Google preview (Inner Product Structures: Theory and Applications By V.I. Istratescu), the other you can hopefully get at your library (Characterizations of . 1 Orthogonal Basis for Inner Product Space If V = P3 with the inner product = R1 −1 f(x)g(x)dx, apply the Gram-Schmidt algorithm to obtain an orthogonal basis from B = {1,x,x2,x3}. 2 Inner-Product Function Space Consider the vector space C[0,1] of all continuously diﬀerentiable functions deﬁned on File Size: KB.

Therefore we have verified that the dot product is indeed an inner product space. Of course, there are many other types of inner products that can be formed on more abstract vector spaces. Such a vector space with an inner product is known as an inner product space which we define below. Inner product space, In mathematics, a vector space or function space in which an operation for combining two vectors or functions (whose result is called an inner product) is defined and has certain properties. Such spaces, an essential tool of functional analysis and vector theory, allow analysis of classes of functions rather than individual functions.

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The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed : Claudi Alsina, Justyna Sikorska, M Santos Tomas.

Characterizations of Inner Product Spaces (Operator Theory Advances and Applications) Softcover reprint of the original 1st ed. Edition by Dan Amir (Author) ISBN ISBN Why is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Format: Paperback. Characterizations of Inner Product Spaces.

Authors (view affiliations) Dan Amir; Book. Characterizations of inner product spaces book Search within book. Front Matter. Pages i-vii. PDF. Introduction. The Parallelogram Equality and Derived Equalities. Dan Amir.

Pages Norm Derivatives Characterizations. Dan Amir. Pages James’ Isoceles Orthogonality (Midpoints of. ISBN: OCLC Number: Description: pages cm. Contents: 2-Dimensional Characterization.- The Parallelogram.

Get this from a library. Characterizations of inner product spaces. [Dan Amir] -- Every mathematician working in Banaeh spaee geometry or Approximation theory knows, from his own experienee, that most "natural" geometrie properties may faH to hold in a generalnormed spaee unless.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. Chesterton.

The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The. Characterizations of Inner Product Spaces. Authors: Amir. Free Preview. Buy this book eB49 Blaschke’s Condition and Derived Characterizations.

*immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of the ebook. Only valid.

The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical.

The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces.

Since the appearance of Jordan-von Neumann's classical theorem (The. Preview this book» What people are Other Norm Characterizations of Inner Product Structures. Orthogonality in Normed Linear Spaces and Characterizations of Inner Product Spaces. Approximation Theory and Characterizations of Inner Product Spaces.

Characterizations of inner product spaces. Mathematics of computing. Discrete mathematics. Graph theory. Trees. Mathematical analysis. Numerical analysis. Probability and statistics.

Probabilistic reasoning algorithms. Random number generation. Theory of computation. Randomness, geometry and discrete structures. CHARACTERIZATIONS OF INNER PRODUCT SPACES 87 B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math.

Dokl. 7 (), 72– J. R¨atz, Characterizations of inner product spaces by means of orthogonally additive map-pings, Aequationes Math.

58 (), – 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. As the main tool, we use a fixed point theorem for the function spaces.

We finish the paper with some new inequalities characterizing the inner product spaces. Introduction. In the literature there are many characterizations of inner product spaces. The first norm characterization of inner product space was given by Fréchet in Cited by: Book Description In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces.

They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied. Theorem gives a characterization of inner product spaces in terms of equality of best approximation and best coapproximation on one dimensional subspaces of the space.

In Theorem we prove the speciality of \((R^n,\Vert ~\Vert _2)\) among \((R^n,\Vert ~\Vert _p)\) spaces, in terms of the existence of strongly orthonormal Hamel basis in Cited by: Norm Derivatives and Characterizations of Inner Product Spaces Claudi Alsina, Justyna Sikorska, M.

Santos Tomas The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces.

that X is an inner product space if and only if it is true that whenever x,y are points in ∂B such that the line through x and y supports √ 2 2 B then x ⊥ y in the sense of Birkhoﬀ.

Introduction Several known characterizations of inner product spaces are available in the literature [1]. This paper concerns a new characterization by. In Section 4 of [3], Durier extends a couple of characterizations of inner product spaces (in short, IPS) given by Amir in his classical book [1].

Our study led us to try to understand as well as possible Amir’s originalcharacterizations,and so let us beginwith them. We ﬁrst need some notations. Inner-Product Spaces, Euclidean Spaces As in Chap.2, the term “linear space” will be used as a shorthand for “ﬁnite dimensional linear space over R”.

However, the deﬁnitions of an inner-product space and a Euclidean space do not really require ﬁnite-dimensionality. Many of the results, for example the Inner-Product In.By Dan Amir: pp. SFr–. (Birkhäuser Verlag, )Cited by: SOME CHARACTERIZATIONS OF INNER-PRODUCT SPACES BY MAHLON M.

DAY 1. Introduction. The theorems of this paper give a number of conditions under which the norm in a real-linear or complex-linear normed space can be defined from an inner product. It should be emphasized that these are not.