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 2092
The relation of being quasi - nilpotent equivalent is indeed an equivalence
relation and , when T and U are quasi - nilpotent equivalent , then ( i ) o ( T ) = 0 (
U ) , ( ii ) T has the single valued extension property if and only if U does , and ( iii
) if T ...
The relation of being quasi - nilpotent equivalent is indeed an equivalence
relation and , when T and U are quasi - nilpotent equivalent , then ( i ) o ( T ) = 0 (
U ) , ( ii ) T has the single valued extension property if and only if U does , and ( iii
) if T ...
Page 2105
is a norm equivalent to 1 : 1 and relative to which all the operators E ( 8 ) become
Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the
compact support K of E , then 11 56 ( 8 ) E ( ds ) || = sup || ( ) SEK Berkson [ 2 ] ...
is a norm equivalent to 1 : 1 and relative to which all the operators E ( 8 ) become
Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the
compact support K of E , then 11 56 ( 8 ) E ( ds ) || = sup || ( ) SEK Berkson [ 2 ] ...
Page 2115
It is proved that if T is decomposable and T and U are quasi - nilpotent equivalent
, then U is decomposable . Moreover , if T and U are decomposable , then XT ( F )
= Xu ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...
It is proved that if T is decomposable and T and U are quasi - nilpotent equivalent
, then U is decomposable . Moreover , if T and U are decomposable , then XT ( F )
= Xu ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...
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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 |