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 2108
Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A . Then
in order for there to exist a necessarily unique spectral measure d on the Baire
sets in X X Y to A such that ( 8 x 0 ) = u ( 8 ) v ( o ) for all 8 , o , it is necessary and
...
Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A . Then
in order for there to exist a necessarily unique spectral measure d on the Baire
sets in X X Y to A such that ( 8 x 0 ) = u ( 8 ) v ( o ) for all 8 , o , it is necessary and
...
Page 2278
There exists a unique multiplicity function m defined on B * with the property that
for each F * € C * , m ( F * ) is the least cardinal power of a set of cyclic subspaces
spanning F * X * in the X - topology . There is a unique decomposition of the ...
There exists a unique multiplicity function m defined on B * with the property that
for each F * € C * , m ( F * ) is the least cardinal power of a set of cyclic subspaces
spanning F * X * in the X - topology . There is a unique decomposition of the ...
Page 2405
If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the integral ( Ah ) ( 8 ) = S 14 ( 8 , t
) | h ( ) u ( dt ) ( 14 ) exists for u - almost all s , and that , writing fl . for the norm of
an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...
If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the integral ( Ah ) ( 8 ) = S 14 ( 8 , t
) | h ( ) u ( dt ) ( 14 ) exists for u - almost all s , and that , writing fl . for the norm of
an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...
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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 |