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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Results 1-3 of 84
Page 1947
Let B , , . . . , 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 B , , . . . , 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
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 . XVII . 2 . 10 ) that TƯxe ) x = T ( xe ) E ( 8 ) 2 = T ( Xe = ) 2
...
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 . XVII . 2 . 10 ) that TƯxe ) x = T ( xe ) E ( 8 ) 2 = T ( Xe = ) 2
...
Page 2361
Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob
Theodore Schwartz. are simple poles of the resolvent function R ( u ; T ' ) . Let U ,
be a sequence of bounded domains covering the whole complex plane , and ...
Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob
Theodore Schwartz. are simple poles of the resolvent function R ( u ; T ' ) . Let U ,
be a sequence of bounded domains covering the whole complex plane , and ...
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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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Common terms and phrases
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 |