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 2160
... and this limit is clearly zero . Thus ( 1o I – T ' ) y = 0 . It will next be shown that
the vector x - y is in the closure of the manifold ( 101 – T ' ) X . To see this it will , in
view of Corollary II . 3 . 13 , suffice to show that x * ( x - y ) = 0 for every linear ...
... and this limit is clearly zero . Thus ( 1o I – T ' ) y = 0 . It will next be shown that
the vector x - y is in the closure of the manifold ( 101 – T ' ) X . To see this it will , in
view of Corollary II . 3 . 13 , suffice to show that x * ( x - y ) = 0 for every linear ...
Page 2226
315 ) has shown that in a complete metrizable locally convex space there may
not be a single functional corresponding to x * ; however , some of the results
presented here can still be generalized . Walsh [ 1 ] showed that if A is a complex
B ...
315 ) has shown that in a complete metrizable locally convex space there may
not be a single functional corresponding to x * ; however , some of the results
presented here can still be generalized . Walsh [ 1 ] showed that if A is a complex
B ...
Page 2360
It will be shown below that | T ' ' R ( u ; T ) A S | for u in V , and i sufficiently large .
From this it will then follow as above that the function f ( u ) = R ( u ; T + P ) f is
uniformly bounded . It will also be shown that T - v is compact . From this , ( iii ) ,
and ...
It will be shown below that | T ' ' R ( u ; T ) A S | for u in V , and i sufficiently large .
From this it will then follow as above that the function f ( u ) = R ( u ; T + P ) f is
uniformly bounded . It will also be shown that T - v is compact . From this , ( iii ) ,
and ...
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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 |