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 2021
18 I s Equation ( 24 ) shows that | s \ - - Â ( s ) is unitary for 8 + 0 . Thus ( 40 ) * = 1
, 0 8€ 8° . ( 25 ) A - + 6 ) = ( . ) 0 + Se RP and ( 26 ) TÂ ( s ) ¥ ( 8 ) | = 18114 ( s ) ] ,
SE S , WE H2 . The equation Ap = 0 , being equivalent to the Cauchy - Riemann ...
18 I s Equation ( 24 ) shows that | s \ - - Â ( s ) is unitary for 8 + 0 . Thus ( 40 ) * = 1
, 0 8€ 8° . ( 25 ) A - + 6 ) = ( . ) 0 + Se RP and ( 26 ) TÂ ( s ) ¥ ( 8 ) | = 18114 ( s ) ] ,
SE S , WE H2 . The equation Ap = 0 , being equivalent to the Cauchy - Riemann ...
Page 2074
Now let y be an arbitrary vector in H . and define the vector x by the equation ( 36
) . Then ( 31 ) shows that x is in H . and equation ( 35 ) holds . This means that for
some vector 2 in H - we have e519 - by = e - Be - 569 + x + 2 , and , using ( 30 ) ...
Now let y be an arbitrary vector in H . and define the vector x by the equation ( 36
) . Then ( 31 ) shows that x is in H . and equation ( 35 ) holds . This means that for
some vector 2 in H - we have e519 - by = e - Be - 569 + x + 2 , and , using ( 30 ) ...
Page 2401
( 2 ) ( 5 ) assuming that U has the form U = I + T ( B ) , with Be A . Taking U to be of
this form , we see that equation ( 1 ) is equivalent to the equation ( I + T ( B ) ) ( T +
( A2 ) ) = T ( I + T ( B ) ) , that is , to ( 3 ) T ( B ) T – TT ( B ) = - 1 ( B ) q ( A4 ) — 9 ...
( 2 ) ( 5 ) assuming that U has the form U = I + T ( B ) , with Be A . Taking U to be of
this form , we see that equation ( 1 ) is equivalent to the equation ( I + T ( B ) ) ( T +
( A2 ) ) = T ( I + T ( B ) ) , that is , to ( 3 ) T ( B ) T – TT ( B ) = - 1 ( B ) q ( A4 ) — 9 ...
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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 |