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 1979
It follows from equations ( iv ) and ( v ) of Lemma 3 that Ey ( s ) ; Â ( s ) ) is e -
essentially bounded on S . Lemma 4 then shows that condition ( i ) of the theorem
is satisfied . Q . E . D . 8 COROLLARY . Every operator A in AP is the strong limit
of ...
It follows from equations ( iv ) and ( v ) of Lemma 3 that Ey ( s ) ; Â ( s ) ) is e -
essentially bounded on S . Lemma 4 then shows that condition ( i ) of the theorem
is satisfied . Q . E . D . 8 COROLLARY . Every operator A in AP is the strong limit
of ...
Page 2169
This shows that ( vi ) holds for every bounded Borel function f and every
continuous function g . A repetition of this argument shows that it also holds if f
and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T )
commute and ...
This shows that ( vi ) holds for every bounded Borel function f and every
continuous function g . A repetition of this argument shows that it also holds if f
and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T )
commute and ...
Page 2170
These lemmas will show that the hypotheses of Theorem 5 . 18 are satisfied by a
... If a is not real , an expansion of the scalar product ( ( al – T ) » , ( al – T ' ) x )
shows that | ( al — T ' ) < / 2 = \ I ( ) a [ 2 + | ( R ( Q ) I – T ) « [ ? 2 | ( a ) / 2 [ 2 / 2 , so
...
These lemmas will show that the hypotheses of Theorem 5 . 18 are satisfied by a
... If a is not real , an expansion of the scalar product ( ( al – T ) » , ( al – T ' ) x )
shows that | ( al — T ' ) < / 2 = \ I ( ) a [ 2 + | ( R ( Q ) I – T ) « [ ? 2 | ( a ) / 2 [ 2 / 2 , so
...
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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 |