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 2209
The weakly closed operator algebra generated by a o - complete Boolean
algebra B which satisfies the condition of the preceding lemma is the same as the
uniformly closed algebra generated by B . Proof . It is clear that every element in
the ...
The weakly closed operator algebra generated by a o - complete Boolean
algebra B which satisfies the condition of the preceding lemma is the same as the
uniformly closed algebra generated by B . Proof . It is clear that every element in
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 2217
Let X ( x ) , Xy ( 2 ) be the closed linear manifolds generated by the sets { EX Ee B
} , { Ex Ee Bl } , respectively . Since B , is the strong closure of B , each element Ex
with E in B , is contained in X ( x ) and thus X ( x ) 2 X ( 2 ) . Evidently X ( x ) = x ...
Let X ( x ) , Xy ( 2 ) be the closed linear manifolds generated by the sets { EX Ee B
} , { Ex Ee Bl } , respectively . Since B , is the strong closure of B , each element Ex
with E in B , is contained in X ( x ) and thus X ( x ) 2 X ( 2 ) . Evidently X ( x ) = x ...
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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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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 |