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 2149
If the resolvent set is dense , then any two analytic , or even continuous ,
extensions of R ( A ; T ) x must coincide on their common domain of continuity . Q
. E . D . All of the special type operators to be considered in the present section
will have ...
If the resolvent set is dense , then any two analytic , or even continuous ,
extensions of R ( A ; T ) x must coincide on their common domain of continuity . Q
. E . D . All of the special type operators to be considered in the present section
will have ...
Page 2156
are both dense in X . Since M , is dense in X , the manifold ( jI – T ) NM , + { x | ( 1 ,
1 – T ) ^ 2 = 0 } is dense in X , so that ( 141 – T ) ^ ( 12 I – T ) NX + { x | ( 1 , 1 – T )
^ x = 0 } + { x | ( 121 – T ) Nx = 0 } is also dense in X . By Lemma 7 , g ( x ) < y if ...
are both dense in X . Since M , is dense in X , the manifold ( jI – T ) NM , + { x | ( 1 ,
1 – T ) ^ 2 = 0 } is dense in X , so that ( 141 – T ) ^ ( 12 I – T ) NX + { x | ( 1 , 1 – T )
^ x = 0 } + { x | ( 121 – T ) Nx = 0 } is also dense in X . By Lemma 7 , g ( x ) < y if ...
Page 2159
The union of all intervals of constancy relative to T is an open set dense in I . .
PROOF . It is clear that the union of intervals of constancy is open . To see that it
is dense , let y be a closed subarc of I , having positive length and let Yn = { 10 /
10 ...
The union of all intervals of constancy relative to T is an open set dense in I . .
PROOF . It is clear that the union of intervals of constancy is open . To see that it
is dense , let y be a closed subarc of I , having positive length and let Yn = { 10 /
10 ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 other sections not shown
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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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact 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 |