Linear Operators, Part 2 |
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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
Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes C , of operators of the mappings p and n of
the previous lemma . We will also write r = ( p + n ) / 2 . We note the following
corollary .
Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes C , of operators of the mappings p and n of
the previous lemma . We will also write r = ( p + n ) / 2 . We note the following
corollary .
Page 1301
If the assertion of the corollary were false , it would follow that has a boundary
value at a which is independent of the set A . , . . . , An - 1 , and hence has at least
n + 1 independent boundary values at a . But this is impossible by Corollary 22 .
If the assertion of the corollary were false , it would follow that has a boundary
value at a which is independent of the set A . , . . . , An - 1 , and hence has at least
n + 1 independent boundary values at a . But this is impossible by Corollary 22 .
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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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 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 give 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
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Bibliographic information
| Title | Linear Operators, Part 2 Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Issue 7 of Pure and applied mathematics; a series of monographs and textbooks |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0471226386, 9780471226383 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |