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 2150
Since the spectrum is totally disconnected , every spectral point is contained in a
spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily
small diameter . Since it is clear that every subset of the resolvent set is an S ( T )
set ...
Since the spectrum is totally disconnected , every spectral point is contained in a
spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily
small diameter . Since it is clear that every subset of the resolvent set is an S ( T )
set ...
Page 2234
The first statement follows from Definition 8 and the three paragraphs of
explanation which precede it , and from Lemma 6 . Statement ( i ) follows from
Corollary 7 . If e is a bounded Borel set with closure contained in U , it may be
supposed ...
The first statement follows from Definition 8 and the three paragraphs of
explanation which precede it , and from Lemma 6 . Statement ( i ) follows from
Corollary 7 . If e is a bounded Borel set with closure contained in U , it may be
supposed ...
Page 2256
Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .
Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an
arbitrarily small compact subset o of o ( T ) which is open in the relative topology
of o ( T ' ) ...
Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .
Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an
arbitrarily small compact subset o of o ( T ) which is open in the relative topology
of o ( T ' ) ...
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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 |