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 |
From inside the book
Results 1-3 of 67
Page 1979
Every operator A in AP is the strong limit of a sequence of spectral operators .
PROOF . Let Sk and Ek be as in the proof of the theorem and let Âx ( s ) = Â ( s ) ,
se SK , = 0 , 8€ SK , so that Âx is in û ” . The corresponding operator Ax = SS Â ( s
) ...
Every operator A in AP is the strong limit of a sequence of spectral operators .
PROOF . Let Sk and Ek be as in the proof of the theorem and let Âx ( s ) = Â ( s ) ,
se SK , = 0 , 8€ SK , so that Âx is in û ” . The corresponding operator Ax = SS Â ( s
) ...
Page 2292
... eigenvectors of T corresponding to the eigenvalue do . If Eldo ; T ) = E ( 20 ) is
the idempotent function of T corresponding to the analytic function which is one
near do and zero elsewhere near the spectrum of T and near infinity , then E ( No
) ...
... eigenvectors of T corresponding to the eigenvalue do . If Eldo ; T ) = E ( 20 ) is
the idempotent function of T corresponding to the analytic function which is one
near do and zero elsewhere near the spectrum of T and near infinity , then E ( No
) ...
Page 2305
8 , 0 ( L ) is the set of numbers in = ( n tæt B + 1 ) ( n + & + B ) , and each
eigenspace corresponding to these eigenvalues is one - dimensional . It follows
immediately from Corollary 9 that L + B is a spectral operator for each bounded
operator ...
8 , 0 ( L ) is the set of numbers in = ( n tæt B + 1 ) ( n + & + B ) , and each
eigenspace corresponding to these eigenvalues is one - dimensional . It follows
immediately from Corollary 9 that L + B is a spectral operator for each bounded
operator ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly 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 |