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 2209
The uniformly closed operator algebra generated by a complete Boolean algebra
B of projections in a B - space X consists of ... It is clear that every operator in the
uniformly closed algebra generated by B has the required invariance property .
The uniformly closed operator algebra generated by a complete Boolean algebra
B of projections in a B - space X consists of ... It is clear that every operator in the
uniformly closed algebra generated by B has the required invariance property .
Page 2361
Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show
that F * ( a ) = ( ( T + P ) * — XI ) -18 * is uniformly bounded for each fe S . ( ( T + P
) * ) . However , in the course of the proof of Theorem 6 it was established that ...
Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show
that F * ( a ) = ( ( T + P ) * — XI ) -18 * is uniformly bounded for each fe S . ( ( T + P
) * ) . However , in the course of the proof of Theorem 6 it was established that ...
Page 2382
We shall now show that the second expression on the right of ( 14 ) converges to
zero as lol → 00 , remaining in P + , uniformly for 0 St < 0 . Let { qn } be a
sequence of functions in C [ 0 , 0 ) , each vanishing outside a bounded subset of [
0 , 0 ) ...
We shall now show that the second expression on the right of ( 14 ) converges to
zero as lol → 00 , remaining in P + , uniformly for 0 St < 0 . Let { qn } be a
sequence of functions in C [ 0 , 0 ) , each vanishing outside a bounded subset of [
0 , 0 ) ...
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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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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 |