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 2300
Then , since the collection of finite sums of projections E ( n ; T ' ) is uniformly
bounded , it is clear from [ * ] that the ... Moreover , Erap ( Elan ; T ) – Elun ; T + P )
) clearly converges uniformly for p 2 K and approaches zero in norm as p →00 .
Then , since the collection of finite sums of projections E ( n ; T ' ) is uniformly
bounded , it is clear from [ * ] that the ... Moreover , Erap ( Elan ; T ) – Elun ; T + P )
) clearly converges uniformly for p 2 K and approaches zero in norm as p →00 .
Page 2361
Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show
that F * ( a ) = ( ( T + P ) * — XI ) - 18 * is uniformly bounded for each fe Sm ( ( T +
P ) * ) . However , in the course of the proof of Theorem 6 it was established that ...
Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show
that F * ( a ) = ( ( T + P ) * — XI ) - 18 * is uniformly bounded for each fe Sm ( ( T +
P ) * ) . However , in the course of the proof of Theorem 6 it was established that ...
Page 2382
We shall now show that the second expression on the right of ( 14 ) converges to
zero as 14 →00 , ji remaining in P + , uniformly for 0 St < oo . Let { an } be a
sequence of functions in Co [ 0 , 0 ) , each vanishing outside a bounded subset of
[ 0 ...
We shall now show that the second expression on the right of ( 14 ) converges to
zero as 14 →00 , ji remaining in P + , uniformly for 0 St < oo . Let { an } be a
sequence of functions in Co [ 0 , 0 ) , each vanishing outside a bounded subset of
[ 0 ...
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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 |