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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Results 1-3 of 85
Page 1948
The sum and the product of two commuting bounded spectral operators in Hilbert
space are also spectral operators . The proof of this corollary will use the
following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space
with A ...
The sum and the product of two commuting bounded spectral operators in Hilbert
space are also spectral operators . The proof of this corollary will use the
following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space
with A ...
Page 2098
when N is a quasi - nilpotent which may not commute with T . The conditions
imply that o ( T ) = 0 , ( T ) . ... ( T ) = [ 0 , 1 ] with a bounded commuting strongly
continuous family E ( t ) , te [ 0 , 1 ] , of projections such that ( i ) E ( 0 ) = 0 , E ( 1 )
= I , ( ii ) ...
when N is a quasi - nilpotent which may not commute with T . The conditions
imply that o ( T ) = 0 , ( T ) . ... ( T ) = [ 0 , 1 ] with a bounded commuting strongly
continuous family E ( t ) , te [ 0 , 1 ] , of projections such that ( i ) E ( 0 ) = 0 , E ( 1 )
= I , ( ii ) ...
Page 2177
Introduction The sum and product of two commuting bounded normal operators
in Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen
that this principle could be extended to the sum and product of two commuting ...
Introduction The sum and product of two commuting bounded normal operators
in Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen
that this principle could be extended to the sum and product of two commuting ...
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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 |