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 88
Page 2203
Let e be an open subset of 1 , let x and 2 * be elements of X , X * , respectively ,
and let z > 0 . Then , because of the regularity of xA ( • ) x * , there is a closed
subset 8 of e such that ( i ) | A ( 81 ) * * — XA ( e ) * * / < E , for every Borel set & ,
with ...
Let e be an open subset of 1 , let x and 2 * be elements of X , X * , respectively ,
and let z > 0 . Then , because of the regularity of xA ( • ) x * , there is a closed
subset 8 of e such that ( i ) | A ( 81 ) * * — XA ( e ) * * / < E , for every Borel set & ,
with ...
Page 2256
Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .
Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an
arbitrarily small compact subset o of o ( T ) which is open in the relative topology
of o ( T ' ) ...
Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .
Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an
arbitrarily small compact subset o of o ( T ) which is open in the relative topology
of o ( T ' ) ...
Page 2309
Our next step is consequently to define such series and develop some of their
basic properties . 4 DEFINITION . ( a ) Let R be an unbounded subset of the
complex plane . Let R , be a subset of the complex plane , and f a function
defined in RX ...
Our next step is consequently to define such series and develop some of their
basic properties . 4 DEFINITION . ( a ) Let R be an unbounded subset of the
complex plane . Let R , be a subset of the complex plane , and f a function
defined in RX ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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Common terms and phrases
analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex 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 formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm 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 statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly 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 |