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 2125
Borel sets and if X , Y EH , then ( P ( 8 ) x , y ) = £ ( P ( x ) x , y ) . ( iv ) The sets { P (
8 ) / 8 e D ( P ) } and { P ( 8 ) * 18 € D ( P ) } are total on H . It is proved that every g
. s . m . can be extended to a class Do ( P ) of Borel subsets of C which is ...
Borel sets and if X , Y EH , then ( P ( 8 ) x , y ) = £ ( P ( x ) x , y ) . ( iv ) The sets { P (
8 ) / 8 e D ( P ) } and { P ( 8 ) * 18 € D ( P ) } are total on H . It is proved that every g
. s . m . can be extended to a class Do ( P ) of Borel subsets of C which is ...
Page 2202
4 that there is a spectral measure A in X * defined on the Borel sets in 1 and such
that xT ( f ] ... It will now be shown that , because of the completeness of B , the
operator A ( e ) is , for every Borel set e , the adjoint of a projection in B . To this
end ...
4 that there is a spectral measure A in X * defined on the Borel sets in 1 and such
that xT ( f ] ... It will now be shown that , because of the completeness of B , the
operator A ( e ) is , for every Borel set e , the adjoint of a projection in B . To this
end ...
Page 2233
By virtue of the equation f ( T | E ( e ) X ) x = f ( T | E ( ē ) X ) , which has been
established for x in E ( e ) X n Esē ) X , we may define a single valued linear
operator Qo on Ue E ( e ) X , where e varies over the family of bounded Borel sets
whose ...
By virtue of the equation f ( T | E ( e ) X ) x = f ( T | E ( ē ) X ) , which has been
established for x in E ( e ) X n Esē ) X , we may define a single valued linear
operator Qo on Ue E ( e ) X , where e varies over the family of bounded Borel sets
whose ...
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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 |