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 2410
Then there exists a positive constant ε = e ( p , D ) depending only on p and D
such that if | | A | | < € ( p , D ) it follows that the operator T + 9 ( A ) is similar to the
operator T and is therefore a spectral operator of scalar type . The following ...
Then there exists a positive constant ε = e ( p , D ) depending only on p and D
such that if | | A | | < € ( p , D ) it follows that the operator T + 9 ( A ) is similar to the
operator T and is therefore a spectral operator of scalar type . The following ...
Page 2439
1 | Ok , ak , Let us now note that there exists a positive absolute constant c such
that ( 31 ) lw - aw ' l 2 cw - w ' | | for all 0 < a < 1 and all w , w ' e £ . Indeed , if 0 is
the angle between w and w ' , it is clear that sw - aw ' | > 1 if 77 / 2 510 ST , while ...
1 | Ok , ak , Let us now note that there exists a positive absolute constant c such
that ( 31 ) lw - aw ' l 2 cw - w ' | | for all 0 < a < 1 and all w , w ' e £ . Indeed , if 0 is
the angle between w and w ' , it is clear that sw - aw ' | > 1 if 77 / 2 510 ST , while ...
Page 2441
This shows that there exists a finite absolute constant c ' such that 1 ( a ) c ' ( 1 +
lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite
constant M " independent of ε such that ( 43 ) 17 6 . + younger og levererar o ...
This shows that there exists a finite absolute constant c ' such that 1 ( a ) c ' ( 1 +
lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite
constant M " independent of ε such that ( 43 ) 17 6 . + younger og levererar o ...
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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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Common terms and phrases
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 |