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 1936
... spectral operator if and only if each restriction T | E , X is a spectral operator . If
T is a spectral operator , then the resolution of the identity for the restriction T | E ,
X is the corresponding restriction of the resolution of the identity for T . PROOF .
... spectral operator if and only if each restriction T | E , X is a spectral operator . If
T is a spectral operator , then the resolution of the identity for the restriction T | E ,
X is the corresponding restriction of the resolution of the identity for T . PROOF .
Page 2094
Restrictions and quotients . Theorem 3 . 10 shows that if a spectral operator Te B
( X ) is reduced by a closed subspace y 9 X and one of its complements ( that is ,
if T commutes with some projection of X onto Y ) , then the restriction T Y of T to ...
Restrictions and quotients . Theorem 3 . 10 shows that if a spectral operator Te B
( X ) is reduced by a closed subspace y 9 X and one of its complements ( that is ,
if T commutes with some projection of X onto Y ) , then the restriction T Y of T to ...
Page 2228
If o is a Borel set , and T is a spectral operator with resolution of the identity E ,
then the restriction T | E ( 0 ) X of T to E ( 0 ) X is a spectral operator whose
resolution of the identity is the restriction of E to E ( 0 ) X . If o is bounded , T | E ( 0
) X is ...
If o is a Borel set , and T is a spectral operator with resolution of the identity E ,
then the restriction T | E ( 0 ) X of T to E ( 0 ) X is a spectral operator whose
resolution of the identity is the restriction of E to E ( 0 ) X . If o is bounded , T | E ( 0
) X is ...
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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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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 |