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 2118
A generalized scalar operator Te B ( X ) is said to be regular if it has a regular
spectral distribution . Although it is not known whether or not every generalized
scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given any
two ...
A generalized scalar operator Te B ( X ) is said to be regular if it has a regular
spectral distribution . Although it is not known whether or not every generalized
scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given any
two ...
Page 2158
If the set of points regular relative to T is dense on To , then every closed
subinterval of To whose end points are regular relative to T is in S ( T ) and every
Borel subset of the plane is measurable T . PROOF . Let y be a closed subinterval
of To ...
If the set of points regular relative to T is dense on To , then every closed
subinterval of To whose end points are regular relative to T is in S ( T ) and every
Borel subset of the plane is measurable T . PROOF . Let y be a closed subinterval
of To ...
Page 2160
1 - T ) X . Since do is interior to an interval of constancy relative to T , it is
therefore a regular point relative to T . Q . E . D . 14 LEMMA ( G ) . If X is reflexive
and if the adjoint T * satisfies the boundedness condition ( B ) , then the regular
points ...
1 - T ) X . Since do is interior to an interval of constancy relative to T , it is
therefore a regular point relative to T . Q . E . D . 14 LEMMA ( G ) . If X is reflexive
and if the adjoint T * satisfies the boundedness condition ( B ) , then the regular
points ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 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 contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit 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 |