Linear Operators: Spectral theory |
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Page 898
If we put E ( 8 ) = 0 when d n ( T ) is void , then Corollary 4 follows immediately
from Theorem 1 and Corollary IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquely
defined spectral measure associated , in Corollary 4 , with the normal operator T
is ...
If we put E ( 8 ) = 0 when d n ( T ) is void , then Corollary 4 follows immediately
from Theorem 1 and Corollary IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquely
defined spectral measure associated , in Corollary 4 , with the normal operator T
is ...
Page 1142
14 . Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes Co of operators of the mappings p and n of
the previous lemma . We will also write t ( p + n ) 2 . We note the following
corollary .
14 . Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes Co of operators of the mappings p and n of
the previous lemma . We will also write t ( p + n ) 2 . We note the following
corollary .
Page 1301
Proceeding inductively we see that vk ) ( b ) = 0 , 0 Sk < 2n - 1 . However , as vo
satisfies an equation of order 2n , v , must be identically zero . This contradiction
completes the proof . Q . E . D . 23 COROLLARY . Let t be a formal differential ...
Proceeding inductively we see that vk ) ( b ) = 0 , 0 Sk < 2n - 1 . However , as vo
satisfies an equation of order 2n , v , must be identically zero . This contradiction
completes the proof . Q . E . D . 23 COROLLARY . Let t be a formal differential ...
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Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Compact Groups | 945 |
Copyright | |
46 other sections not shown
Other editions - View all
Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators: Spectral theory Part 2 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press Volume 7 of Pure and applied mathematics Wiley Classics Library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Contributor | Karreman Mathematics Research Collection |
| Publisher | Interscience Publishers, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |