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 2239
Moreover , statement ( g ) follows from Corollary 7 . ... If T ( f ) is bounded , it follows that the family of operators T ' ( fxe ) is uniformly bounded and hence , by Theorem XVII.2.10 , that the family of functions fXe , e e E ...
Moreover , statement ( g ) follows from Corollary 7 . ... If T ( f ) is bounded , it follows that the family of operators T ' ( fxe ) is uniformly bounded and hence , by Theorem XVII.2.10 , that the family of functions fXe , e e E ...
Page 2246
( n ) ( . it follows that R ( A ) is a bounded operator whose range is contained in the domain of C. It is clear then that ( W –C ) R ( 1 ) . x for x in H and R ( A ) ( AI –C ) .x = x for x in D ( C ) , so that R ( A ) = R ( A ; C ) and ...
( n ) ( . it follows that R ( A ) is a bounded operator whose range is contained in the domain of C. It is clear then that ( W –C ) R ( 1 ) . x for x in H and R ( A ) ( AI –C ) .x = x for x in D ( C ) , so that R ( A ) = R ( A ; C ) and ...
Page 2459
Statement ( b ) of our lemma follows at once . If xn € Lac ( H ) and limno Xn = x , then , by what we ... Thus statement ( a ) of our theorem follows . ... If ( il – H ) - Lac ( H ) were not dense in Lac ( H ) , it would follow by the ...
Statement ( b ) of our lemma follows at once . If xn € Lac ( H ) and limno Xn = x , then , by what we ... Thus statement ( a ) of our theorem follows . ... If ( il – H ) - Lac ( H ) were not dense in Lac ( H ) , it would follow by the ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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Common terms and phrases
adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector 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 |