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 2144
It clearly preserves finite disjoint unions , takes complements into complements ,
is countably additive in the X topology of X * , and is bounded . It remains only to
show that A ( 0 ) A ( S ) = A ( od ) . It is seen , by using the above remarks , that for
...
It clearly preserves finite disjoint unions , takes complements into complements ,
is countably additive in the X topology of X * , and is bounded . It remains only to
show that A ( 0 ) A ( S ) = A ( od ) . It is seen , by using the above remarks , that for
...
Page 2203
The mapping E HO ( E ) is clearly an isomorphism between B and the Boolean
algebra of all open and closed subsets of 1 . These open and closed sets o ( E )
form a basis for the topology in 1 . To see this , note that sets of the form { a | | ( T ...
The mapping E HO ( E ) is clearly an isomorphism between B and the Boolean
algebra of all open and closed subsets of 1 . These open and closed sets o ( E )
form a basis for the topology in 1 . To see this , note that sets of the form { a | | ( T ...
Page 2278
If E * € & * we define m ( E * ) , the multiplicity of E * , to be the smallest cardinal
power of a set A of vectors such that E * X * is spanned in the X - topology by the
manifolds { N ( x * ) / 2 * € A } . The next lemma establishes the required continuity
...
If E * € & * we define m ( E * ) , the multiplicity of E * , to be the smallest cardinal
power of a set A of vectors such that E * X * is spanned in the X - topology by the
manifolds { N ( x * ) / 2 * € A } . The next lemma establishes the required continuity
...
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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 |