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 2144
It clearly preserves finite disjoint unions , takes complements into complements , is countably additive in the X topology of X * , and is bounded . It remains only to show that A ( 0 ) A ( S ) = A ( 08 ) .
It clearly preserves finite disjoint unions , takes complements into complements , is countably additive in the X topology of X * , and is bounded . It remains only to show that A ( 0 ) A ( S ) = A ( 08 ) .
Page 2203
To see this , note that sets of the form { a || ( T - 1A ) ( 0 ) | < a } , with A in A ( B ) form , by definition , a subbasis for the topology of 1 , and since B generates A ( B ) , the sets o ( E ) form a subbasis for the topology of ...
To see this , note that sets of the form { a || ( T - 1A ) ( 0 ) | < a } , with A in A ( B ) form , by definition , a subbasis for the topology of 1 , and since B generates A ( B ) , the sets o ( E ) form a subbasis for the topology of ...
Page 2281
The results are parallel to those in X. The weaker form of completeness enjoyed by B * leads to a weaker form of the representation theorem , as the relevant topology in X * is now the X - topology . As before we shall suppose for ...
The results are parallel to those in X. The weaker form of completeness enjoyed by B * leads to a weaker form of the representation theorem , as the relevant topology in X * is now the X - topology . As before we shall suppose for ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 other sections not shown
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector 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 |