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 2194
Strongly Closed Algebras and Complete Boolean Algebras In this section an
attempt will be made to characterize the strong closure of a commutative algebra
of spectral operators . It has been observed ( cf . VI . 1 . 5 ) that a convex set in the
...
Strongly Closed Algebras and Complete Boolean Algebras In this section an
attempt will be made to characterize the strong closure of a commutative algebra
of spectral operators . It has been observed ( cf . VI . 1 . 5 ) that a convex set in the
...
Page 2195
A Boolean algebra B of projections in a B - space X is said to be complete ( o -
complete ) as an abstract Boolean algebra if each subset ( sequence ) of B has a
greatest lower bound and a least upper bound in B . The Boolean algebra B is ...
A Boolean algebra B of projections in a B - space X is said to be complete ( o -
complete ) as an abstract Boolean algebra if each subset ( sequence ) of B has a
greatest lower bound and a least upper bound in B . The Boolean algebra B is ...
Page 2217
Let B be a o - complete Boolean algebra of projections in a B - space X , and let B
, be its strong closure . By Lemma 3 , B is bounded and thus B , is also a bounded
Boolean algebra of projections in X . Suppose that B , is not complete .
Let B be a o - complete Boolean algebra of projections in a B - space X , and let B
, be its strong closure . By Lemma 3 , B is bounded and thus B , is also a bounded
Boolean algebra of projections in X . Suppose that B , is not complete .
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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 |