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 2082
50 ( McCarthy ) Continuing the preceding exercise , let x4 , xo , and o . be chosen
so that ... Letting 0 and Y be operators defined on L1 ( 01 , M ) and L . ( 01 , M ) as
in the preceding exercise , show that Yis a one - to - one and bicontinuous ...
50 ( McCarthy ) Continuing the preceding exercise , let x4 , xo , and o . be chosen
so that ... Letting 0 and Y be operators defined on L1 ( 01 , M ) and L . ( 01 , M ) as
in the preceding exercise , show that Yis a one - to - one and bicontinuous ...
Page 2172
8 ( Fixman ) Let T be as in the preceding exercise and let op in ( 1 . ) * be a
Banach limit as in Exercise II . 4 . 22 . Let A be defined on lo by Ax = A ( $ 1 , 82 ,
83 , . . . ) = ( g ( x ) , 0 , 0 , . . . ) . Show that A2 = 0 and that p ( TX ) = 9 ( x ) and AT
= TA .
8 ( Fixman ) Let T be as in the preceding exercise and let op in ( 1 . ) * be a
Banach limit as in Exercise II . 4 . 22 . Let A be defined on lo by Ax = A ( $ 1 , 82 ,
83 , . . . ) = ( g ( x ) , 0 , 0 , . . . ) . Show that A2 = 0 and that p ( TX ) = 9 ( x ) and AT
= TA .
Page 2489
1 / 2 ( Hint : Use ( c ) and ( e ) of the preceding exercise . ) 19 Let H be a self
adjoint operator in Hilbert space . Let V be an operator of trace class , and put H ,
= H + V . Put U : = exp ( itH , ) exp ( - itH ) . Let we { ac ( H ) and | | W | | # < 00 ( cf .
1 / 2 ( Hint : Use ( c ) and ( e ) of the preceding exercise . ) 19 Let H be a self
adjoint operator in Hilbert space . Let V be an operator of trace class , and put H ,
= H + V . Put U : = exp ( itH , ) exp ( - itH ) . Let we { ac ( H ) and | | W | | # < 00 ( cf .
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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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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 |