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 2094
They show that if T is spectral , then T * has a unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( 1 ) where l ' şX ** , then it has a unique resolution of the identity of class ( l ' ) .
They show that if T is spectral , then T * has a unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( 1 ) where l ' şX ** , then it has a unique resolution of the identity of class ( l ' ) .
Page 2183
Moreover , P is evidently a projection in B. The set B is clearly a subalgebra of A ( T ) . Let B denote its closure in the uniform topology of operators . By Theorem XV.4.5 and the fact that a scalar type operator is clearly in the ...
Moreover , P is evidently a projection in B. The set B is clearly a subalgebra of A ( T ) . Let B denote its closure in the uniform topology of operators . By Theorem XV.4.5 and the fact that a scalar type operator is clearly in the ...
Page 2470
Moreover , by this same lemma , we have ( 49 ) || T || 2 = I SS 114 , ( a , b ) / 2 ( da ) u ( db ) . 1.j = 1 R Using ( 48 ) and the fact that fi ( a ) = 0 for a Ely , we have + n 2 ( 50 ) S ** | Testuj ] ? de = SOLS 4 ( a , b ) f ( b ) ...
Moreover , by this same lemma , we have ( 49 ) || T || 2 = I SS 114 , ( a , b ) / 2 ( da ) u ( db ) . 1.j = 1 R Using ( 48 ) and the fact that fi ( a ) = 0 for a Ely , we have + n 2 ( 50 ) S ** | Testuj ] ? de = SOLS 4 ( a , b ) f ( b ) ...
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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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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 |