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 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 2113
Thus the restriction of an operator T to an arbitrary invariant closed subspace
may have spectrum larger than o ( T ) . Foiaş [ 12 ] defined a closed linear
subspace Y of a B - space X to be a spectral maximal subspace of Te B ( X ) if ( i )
V is ...
Thus the restriction of an operator T to an arbitrary invariant closed subspace
may have spectrum larger than o ( T ) . Foiaş [ 12 ] defined a closed linear
subspace Y of a B - space X to be a spectral maximal subspace of Te B ( X ) if ( i )
V is ...
Page 2114
17 ) and if E , is the corresponding projection operator , then E , X is a spectral
maximal subspace of T . Hence both spectral and compact operators have “
many " spectral maximal subspaces . It can be seen that they are decomposable
in the ...
17 ) and if E , is the corresponding projection operator , then E , X is a spectral
maximal subspace of T . Hence both spectral and compact operators have “
many " spectral maximal subspaces . It can be seen that they are decomposable
in the ...
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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 |