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 |
From inside the book
Results 1-3 of 87
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 .
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 .
Page 2189
Hence for an arbitrary g in EB ( 1 , 2 ) , equation ( ii ) holds for every characteristic function f of a set in £ . ... Now Ey is defined and countably additive on the field of Borel sets and it commutes with S ( f ) .
Hence for an arbitrary g in EB ( 1 , 2 ) , equation ( ii ) holds for every characteristic function f of a set in £ . ... Now Ey is defined and countably additive on the field of Borel sets and it commutes with S ( f ) .
Page 2233
Let { en } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( U = 1 ... ( i ) For each Borel set e and each x in D ( f ( T ) ) , E ( e ) D ( ( T ) ) Ç DIS ( T ) ) and E ( e ) s ( T ) .
Let { en } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( U = 1 ... ( i ) For each Borel set e and each x in D ( f ( T ) ) , E ( e ) D ( ( T ) ) Ç DIS ( T ) ) and E ( e ) s ( T ) .
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
Other editions - View all
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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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 |