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 1947
Let B1 , . . . , Bk be a finite collection of commuting bounded Boolean algebras of
projections in a Hilbert space H . Then there exists a bounded self adjoint
operator B in H with a bounded everywhere defined inverse such that BEB - 1 is
a self ...
Let B1 , . . . , Bk be a finite collection of commuting bounded Boolean algebras of
projections in a Hilbert space H . Then there exists a bounded self adjoint
operator B in H with a bounded everywhere defined inverse such that BEB - 1 is
a self ...
Page 2239
... William G. Bade, Robert G. Bartle L. Bers, J. J. Stoker. Since f Xe is a bounded
function , the operator T ( f Xe ) is a bounded operator . If x is in E ( 7 ) X as well
as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf .
... William G. Bade, Robert G. Bartle L. Bers, J. J. Stoker. Since f Xe is a bounded
function , the operator T ( f Xe ) is a bounded operator . If x is in E ( 7 ) X as well
as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf .
Page 2361
Let U , be a sequence of bounded domains covering the whole complex plane ,
and suppose that lim - minze ui 1z1 = 00 . Let Vi be the boundary of U , . Let 0 Sv
< l , and put Mi = max lululaul - 1 . NEV i . UEO ( T ) Let do $ ( T ) , and let P be an
...
Let U , be a sequence of bounded domains covering the whole complex plane ,
and suppose that lim - minze ui 1z1 = 00 . Let Vi be the boundary of U , . Let 0 Sv
< l , and put Mi = max lululaul - 1 . NEV i . UEO ( T ) Let do $ ( T ) , and let P be an
...
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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 |