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 1948
The sum and the product of two commuting bounded spectral operators in Hilbert
space are also spectral operators . The proof of this corollary will use the
following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space
with A ...
The sum and the product of two commuting bounded spectral operators in Hilbert
space are also spectral operators . The proof of this corollary will use the
following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space
with A ...
Page 2098
See also Deal [ 2 ] . The following result was proved by Sine [ 1 ] , using
techniques similar to those in Smart [ 2 ] . Let Te B ( x ) with o ( T ) = 0 . ( T ) = [ 0 ,
1 ] with a bounded commuting strongly continuous family E ( t ) , te [ 0 , 1 ] , of
projections ...
See also Deal [ 2 ] . The following result was proved by Sine [ 1 ] , using
techniques similar to those in Smart [ 2 ] . Let Te B ( x ) with o ( T ) = 0 . ( T ) = [ 0 ,
1 ] with a bounded commuting strongly continuous family E ( t ) , te [ 0 , 1 ] , of
projections ...
Page 2177
Introduction The sum and product of two commuting bounded normal operators
in Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen
that this principle could be extended to the sum and product of two commuting ...
Introduction The sum and product of two commuting bounded normal operators
in Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen
that this principle could be extended to the sum and product of two commuting ...
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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 |