Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1930
4 we have seen that a bounded normal operator in Hilbert space always has a
uniquely defined bounded and countably additive resolution of the identity
defined on the field of all Borel subsets of the plane . The operators we shall
study in the ...
4 we have seen that a bounded normal operator in Hilbert space always has a
uniquely defined bounded and countably additive resolution of the identity
defined on the field of all Borel subsets of the plane . The operators we shall
study in the ...
Page 2144
It clearly preserves finite disjoint unions , takes complements into complements ,
is countably additive in the X topology of X * , and is bounded . It remains only to
show that A ( 0 ) A ( S ) = A ( od ) . It is seen , by using the above remarks , that for
...
It clearly preserves finite disjoint unions , takes complements into complements ,
is countably additive in the X topology of X * , and is bounded . It remains only to
show that A ( 0 ) A ( S ) = A ( od ) . It is seen , by using the above remarks , that for
...
Page 2591
countably additive, XV.2 (1930), XV.2.3 (1930), XV.2.4 (1931) definition of, XV.2.1
(1929) integral with respect to, XV.2 (1929) Spectral operator, adjoint of, XVI.4.6 (
2148), XVI.5. 16 (2162) canonical reduction of, XV.4 (1937), XV.4.5 (1939), ...
countably additive, XV.2 (1930), XV.2.3 (1930), XV.2.4 (1931) definition of, XV.2.1
(1929) integral with respect to, XV.2 (1929) Spectral operator, adjoint of, XVI.4.6 (
2148), XVI.5. 16 (2162) canonical reduction of, XV.4 (1937), XV.4.5 (1939), ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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Common terms and phrases
analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero
Bibliographic information
| Title | Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |