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 1926
Since , as this example shows , the theory of normal operators is not an infallible
guide even to the theory of arbitrary operators in finite dimensional spaces , we
must revert to more general considerations in attempting to construct the desired
...
Since , as this example shows , the theory of normal operators is not an infallible
guide even to the theory of arbitrary operators in finite dimensional spaces , we
must revert to more general considerations in attempting to construct the desired
...
Page 2101
... T ) satisfies a mth order rate of growth condition , then the nilpotent part N of T
is of type m – 1 ; that is , Nm = 0 . This was proved by Dunford [ 18 ] ; however ,
McCarthy [ 1 , I ] showed that this assertion does not hold in an arbitrary B - space
.
... T ) satisfies a mth order rate of growth condition , then the nilpotent part N of T
is of type m – 1 ; that is , Nm = 0 . This was proved by Dunford [ 18 ] ; however ,
McCarthy [ 1 , I ] showed that this assertion does not hold in an arbitrary B - space
.
Page 2193
Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an
arbitrary B - space , for it has been shown by Kakutani [ 15 ] that the sum of two
commuting scalar type spectral operators in a space of continuous functions ...
Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an
arbitrary B - space , for it has been shown by Kakutani [ 15 ] that the sum of two
commuting scalar type spectral operators in a space of continuous functions ...
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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 |