Linear Operators, Part 1: General Theory

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John Wiley & Sons, Feb 23, 1988 - Mathematics - 872 pages
This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis. Dunford and Schwartz emphasize the significance of the relationships between the abstract theory and its applications. This text has been written for the student as well as for the mathematician—treatment is relatively self-contained. This is a paperback edition of the original work, unabridged, in three volumes.

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Contents

Preliminary Concepts
1
B Topological Preliminaries
10
Algebraic Preliminaries
34
Three Basic Principles of Linear Analysis
49
Integration and Set Functions
95
The VitaliHahnSaks Theorem and Spaces of Measures
155
Relativization of Set Functions
164
Exercises
168
Operators and Their Adjoints
475
Adjoints
478
Projections
480
Weakly Compact Operators
482
Compact Operators
485
Operators with Closed Range
487
Representation of Operators in CS
489
The Representation of Operators in a Lebesgue Space
498

The RadonNikodým Theorem
174
Product Measures
183
Differentiation
210
Exercises
222
Functions of a Complex Variable
224
Notes and Remarks
232
Special Spaces
237
A List of Special Spaces
238
Finite Dimensional Spaces
244
Hilbert Space
247
The Spaces BS E and BS
257
The Space CS
261
The Space 4P
281
SPECTRAL THEORY
282
The Spaces LS E u
285
Spaces of Set Functions
305
Vector Valued Measures
318
The Space TMS EM
329
Functions of Bounded Variation
337
Exercises
338
Exercises on Orthogonal Series and Analytic Functions
357
Tabulation of Results
372
BAlgebras
396
Convex Sets and Weak Topologies
409
Linear Topological Spaces
413
Weak Topologies Definitions and Fundamental Properties
418
Weak Topologies Compactness and Reflexivity
423
Weak Topologies Vetrizability Lnbounded Sets 125
430
Exercises
436
Extremal Points
439
Tangent Functionals
445
Fixed Point Theoremis
453
Exercises
457
Notes and Remarks
460
Exercises
511
The Riesz Convexity Theorem
520
Exercises on Inequalities
526
Notes and Remarks
538
General Spectral Theory 355
555
Spectral Theory in a Finite Dimensional Space
556
Exercises
561
Functions of an Operator
566
Spectral Theory of Compact Operators
577
Exercises
580
Perturbation Theory
584
Tauberian Theory
593
Exercises
597
An Operational Calculus for Unbounded Closed Operators
599
Exercises
604
Notes and Remarks
606
Bounded Normal Operators in Hilbert Space
611
Applications
613
Functions of an Infinitesimal Generator
641
Exercises
653
Ergodic Theory
657
Mean Ergodic Theorems
660
Pointwise Ergodic Theorems
668
The Ergodic Theory of Continuous Flows
684
Uniform Ergodic Theory
708
Exercises on Ergodic Theory
717
Notes and Remarks
726
REFERENCES
731
Sufficient Conditions XVII Algebras of Spectral Operators XVIII Unbounded Spectral Operators XIX Perturbations of Spectral Operators with Discre...
735
NOTATION INDEX
827
AUTHOR INDEX
829
SUBJECT INDEX
837
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About the author (1988)

Nelson James Dunford was an American mathematician, known for his work in functional analysis, namely integration of vector valued functions, ergodic theory, and linear operators. The Dunford decomposition, Dunford-Pettis property, and Dunford-Schwartz theorem bear his name.

Jacob Theodore "Jack" Schwartz was an American mathematician, computer scientist, and professor of computer science at the New York University Courant Institute of Mathematical Sciences. He was the designer of the SETL programming language and started the NYU Ultracomputer project.

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