Normed Linear Spaces
Author | : Mahlon M. Day |
Publisher | : Springer Science & Business Media |
Total Pages | : 222 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662090007 |
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Author | : Mahlon M. Day |
Publisher | : Springer Science & Business Media |
Total Pages | : 222 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662090007 |
Author | : |
Publisher | : Elsevier |
Total Pages | : 321 |
Release | : 2011-10-10 |
Genre | : Mathematics |
ISBN | : 0080871798 |
Introduction to Banach Spaces and their Geometry
Author | : J. R. Giles |
Publisher | : Cambridge University Press |
Total Pages | : 298 |
Release | : 2000-03-13 |
Genre | : Mathematics |
ISBN | : 9780521653756 |
This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.
Author | : Rodney Coleman |
Publisher | : Springer Science & Business Media |
Total Pages | : 255 |
Release | : 2012-07-25 |
Genre | : Mathematics |
ISBN | : 1461438942 |
This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.
Author | : E. Suhubi |
Publisher | : Springer Science & Business Media |
Total Pages | : 702 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401701415 |
Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.
Author | : Tsoy-Wo Ma |
Publisher | : World Scientific |
Total Pages | : 378 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9789810221379 |
This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis.
Author | : Vitali D. Milman |
Publisher | : Springer |
Total Pages | : 166 |
Release | : 2009-02-27 |
Genre | : Mathematics |
ISBN | : 3540388222 |
This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie].
Author | : Karen Saxe |
Publisher | : Springer Science & Business Media |
Total Pages | : 209 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475736878 |
The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts.
Author | : Bryan Rynne |
Publisher | : Springer Science & Business Media |
Total Pages | : 276 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1447136551 |
This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.