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 2188
Let E be a spectral measure in the complex B - space X which is defined and
countably additive on a o - field of subsets of a set 1 and let g be a bounded Borel
measurable function defined on the complex plane . Then 2 ) ) E ( d ) ) = l g ( u ) E
...
Let E be a spectral measure in the complex B - space X which is defined and
countably additive on a o - field of subsets of a set 1 and let g be a bounded Borel
measurable function defined on the complex plane . Then 2 ) ) E ( d ) ) = l g ( u ) E
...
Page 2189
Now E , is defined and countably additive on the field of Borel sets and it
commutes with S ( f ) . Thus to see that E , is the resolution of the identity for s ( f )
it will suffice to show that 1 . ( iv ) O ( S ( f ) | E ( 8 ) X ) $ 8 for every Borel set 8 of
complex ...
Now E , is defined and countably additive on the field of Borel sets and it
commutes with S ( f ) . Thus to see that E , is the resolution of the identity for s ( f )
it will suffice to show that 1 . ( iv ) O ( S ( f ) | E ( 8 ) X ) $ 8 for every Borel set 8 of
complex ...
Page 2233
Let T be a spectral operator with resolution of the identity E , and let f be a
function analytic in an open set U such that E ( U ) ... The operator f ( T ) of
Definition 8 is closed , linear , and independent of the particular sequence of
Borel sets used to ...
Let T be a spectral operator with resolution of the identity E , and let f be a
function analytic in an open set U such that E ( U ) ... The operator f ( T ) of
Definition 8 is closed , linear , and independent of the particular sequence of
Borel sets used to ...
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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 |