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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Results 1-3 of 46
Page 2148
If € 8 , then , using ( D ) , the compact set do ( T ) may be covered by a set o in the
field S ( T ) with 1€ 7 . Since T is a spectral operator of class ( S ( T ) , X * ) , we
have o ( T . ) Sõ and consequently , is in p ( T . ) , which means that XI - T is a one
...
If € 8 , then , using ( D ) , the compact set do ( T ) may be covered by a set o in the
field S ( T ) with 1€ 7 . Since T is a spectral operator of class ( S ( T ) , X * ) , we
have o ( T . ) Sõ and consequently , is in p ( T . ) , which means that XI - T is a one
...
Page 2323
Consequently , by factoring out a factor ( iu ) ' , the coefficients ap , bp , Cp of the
terms of order p in the determinant N ( u ) become the same as the coefficients ap
, bp , Cp in the determinant Ñ ( u ) = a , etu + bpe - lu + cp of the matrix ( ÔNak ) ...
Consequently , by factoring out a factor ( iu ) ' , the coefficients ap , bp , Cp of the
terms of order p in the determinant N ( u ) become the same as the coefficients ap
, bp , Cp in the determinant Ñ ( u ) = a , etu + bpe - lu + cp of the matrix ( ÔNak ) ...
Page 2343
Consequently , if we use Lagrange ' s rule to expand this 2v x 2v determinant by
minors of order v , we find that the expansion contains only two non - vanishing
terms . Thus our 2v X 2v determinant may be expressed as P2P , FQ1Q2 , where
...
Consequently , if we use Lagrange ' s rule to expand this 2v x 2v determinant by
minors of order v , we find that the expansion contains only two non - vanishing
terms . Thus our 2v X 2v determinant may be expressed as P2P , FQ1Q2 , where
...
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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 |