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
I ] the following idea is introduced : Let T , U = B ( x ) and let ( T - USB = = ( - 1 ) ^ -
^ ( T + U - 1 ; CO then we say that T and U are quasi - nilpotent equivalent in case
lim ( T – U ) [ n ] | 1 / n = lim | ( U – T ) [ n ] | 11n = 0 . n + 11 + ( It is clear that if U ...
I ] the following idea is introduced : Let T , U = B ( x ) and let ( T - USB = = ( - 1 ) ^ -
^ ( T + U - 1 ; CO then we say that T and U are quasi - nilpotent equivalent in case
lim ( T – U ) [ n ] | 1 / n = lim | ( U – T ) [ n ] | 11n = 0 . n + 11 + ( It is clear that if U ...
Page 2105
Berkson ( 2 ) showed that if E is a bounded spectral measure and if one defines |
| 3 | | = sup { var æ * E ( - ) w | 12 * 1 = 1 } , then | | · | | is a norm equivalent to 1 : 1
and relative to which all the operators E ( 8 ) become Hermitian . It follows from ...
Berkson ( 2 ) showed that if E is a bounded spectral measure and if one defines |
| 3 | | = sup { var æ * E ( - ) w | 12 * 1 = 1 } , then | | · | | is a norm equivalent to 1 : 1
and relative to which all the operators E ( 8 ) become Hermitian . It follows from ...
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 X ( F )
= xy ( 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 X ( F )
= xy ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...
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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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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 |