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 ... 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 ... It is clear that every operator in the uniformly closed algebra generated by B has the required invariance property .
Page 2361
Thus , F * ( A ) is uniformly bounded for in UE Vi , and hence , by the maximum modulus theorem , is uniformly bounded for å in UEN Uj . Since the set { U } , i 2 N , covers the whole plane , with the possible exception of a bounded set ...
Thus , F * ( A ) is uniformly bounded for in UE Vi , and hence , by the maximum modulus theorem , is uniformly bounded for å in UEN Uj . Since the set { U } , i 2 N , covers the whole plane , with the possible exception of a bounded set ...
Page 2382
where Q = So 19 ( 8 ) | ds ; this follows since we have shown above that Luhul 3 2011-12 We shall now show that the second expression on the right of ( 14 ) converges to zero as lel → 00 , remaining in P + , uniformly for 0 St < 0 .
where Q = So 19 ( 8 ) | ds ; this follows since we have shown above that Luhul 3 2011-12 We shall now show that the second expression on the right of ( 14 ) converges to zero as lel → 00 , remaining in P + , uniformly for 0 St < 0 .
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 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 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 |