Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 68
Page 2256
Suppose first that ( a ) and ( b ) are satisfied . Since o ( T ) is totally disconnected ,
there exists a complex number 1 € 0 ( T ) . It is clear that without any loss of
generality we may assume that i = 0 . Let R = T - 1 . Then , by Theorem VII . 9 .
Suppose first that ( a ) and ( b ) are satisfied . Since o ( T ) is totally disconnected ,
there exists a complex number 1 € 0 ( T ) . It is clear that without any loss of
generality we may assume that i = 0 . Let R = T - 1 . Then , by Theorem VII . 9 .
Page 2284
However , rather than seek the maximum generality , it will be convenient to
suppose that B is itself complete and satisfies the countable chain condition .
Both these properties hold for B if X is separable , so this will be assumed for the
rest of ...
However , rather than seek the maximum generality , it will be convenient to
suppose that B is itself complete and satisfies the countable chain condition .
Both these properties hold for B if X is separable , so this will be assumed for the
rest of ...
Page 2303
Suppose that E is its resolution of the identity , and suppose that { an } is an
enumeration of its spectrum . Let dn denote the distance from an to o ( T ) — { an }
. Suppose that for all but a finite number of n , Elan ) has a onedimensional range
.
Suppose that E is its resolution of the identity , and suppose that { an } is an
enumeration of its spectrum . Let dn denote the distance from an to o ( T ) — { an }
. Suppose that for all but a finite number of n , Elan ) has a onedimensional range
.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
Common terms and phrases
algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete 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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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 strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero
Bibliographic information
| Title | Linear Operators: Spectral operators Part 3 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| ISBN | 0471226394, 9780471226390 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |