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 2017
and the fraction in the inequality ( i ) of Theorem 6 is 1si - sl ? ... corresponding
closed operator As cannot be self adjoint , but it always has a resolution of the
identity for 8 ( 8 ) = ( 87 – 83 ) + 4a8 , so that the inequality ( i ) of Theorem 6
holds .
and the fraction in the inequality ( i ) of Theorem 6 is 1si - sl ? ... corresponding
closed operator As cannot be self adjoint , but it always has a resolution of the
identity for 8 ( 8 ) = ( 87 – 83 ) + 4a8 , so that the inequality ( i ) of Theorem 6
holds .
Page 2190
From the preceding lemma it is seen that the map f→ S ( f ) is a continuous
homomorphism of EB ( 1 , 2 ) onto an algebra of scalar type spectral operators .
Thus for some constant K we have | S ( ) < K \ f | and to prove the final inequality
of the ...
From the preceding lemma it is seen that the map f→ S ( f ) is a continuous
homomorphism of EB ( 1 , 2 ) onto an algebra of scalar type spectral operators .
Thus for some constant K we have | S ( ) < K \ f | and to prove the final inequality
of the ...
Page 2399
By ( 44 ) and Hölder ' s inequality we have ( 45 ) { { * ( ( ve ) – ( 0 + 3 ) ( x ) ] 2 due
} " sko { f * 14 1 / 2 L112 | S | 2 . The inequality ( 42a ) follows immediately from (
43 ) and ( 45 ) . Since the inequality ( 42b ) may be deduced in a precisely ...
By ( 44 ) and Hölder ' s inequality we have ( 45 ) { { * ( ( ve ) – ( 0 + 3 ) ( x ) ] 2 due
} " sko { f * 14 1 / 2 L112 | S | 2 . The inequality ( 42a ) follows immediately from (
43 ) and ( 45 ) . Since the inequality ( 42b ) may be deduced in a precisely ...
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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 |