| Reviews |
| - 'The book can be warmly recommended to graduate students of mathematics and physics and also everybody interested in functional analysis.|EMS Newsletter' -
|
| Description | | - · Concisely written modern introduction to functional analysis
- · Provides access to active area of research in functional analysis
| |
The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of HahnBanach. The spaces (p
L
p
(X
,(), C
(X
)' and Sobolov spaces
are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fréchet spaces and their duals. In
particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fréchet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.
|
Readership: Advanced undergraduate/graduate students of mathematics and physics who are familiar with basic university analysis and linear algebra.
| Contents |
Preliminaries
1.
Banach spaces and Metric Linear Spaces
2.
Spectral Theory of Linear Operators
3.
Fréchet Spaces and their Dual Spaces
|
| Authors, editors,
and contributors |
Reinhold Meise, Mathematical Institute, Heinrich Heine University, Dusseldorf and
Dietmar Vogt, Mathematics Faculty, University of Wuppertal
Translated by M. S. Ramanujan
|
| Links to web resources and related information | More in the same subject area:
Functional analysis
|
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limitation price, format, extent, number of illustrations,
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|
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