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
The situation corresponding to an invariant closed subspace of T is not so simple
. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an
invariant closed subspace y of X is spectral if and only if the resolution of the ...
The situation corresponding to an invariant closed subspace of T is not so simple
. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an
invariant closed subspace y of X is spectral if and only if the resolution of the ...
Page 2214
5 , the weakly closed operator algebra W ( B ) generated by B is the same as the
strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit
of finite linear combinations of elements of B . It follows that A leaves invariant ...
5 , the weakly closed operator algebra W ( B ) generated by B is the same as the
strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit
of finite linear combinations of elements of B . It follows that A leaves invariant ...
Page 2286
If M is a closed invariant subspace in X , we denote by 0 ( M ) the closure in H of
the linear set AM , D ( A ) ) . Similarly if K is a closed invariant subspace in H , Y (
K ) denotes the closure in % of A - Kn D ( A - 2 ) ) . It follows from Theorem 19 ( b )
...
If M is a closed invariant subspace in X , we denote by 0 ( M ) the closure in H of
the linear set AM , D ( A ) ) . Similarly if K is a closed invariant subspace in H , Y (
K ) denotes the closure in % of A - Kn D ( A - 2 ) ) . It follows from Theorem 19 ( b )
...
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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 |