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
Thus the strong and weak operator closures of an algebra of operators are the
same . ... Since every scalar type operator is in the strong ( even in the uniform )
closure of the algebra generated by the projections in its resolution of the identity
...
Thus the strong and weak operator closures of an algebra of operators are the
same . ... Since every scalar type operator is in the strong ( even in the uniform )
closure of the algebra generated by the projections in its resolution of the identity
...
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 .
Page 2286
If A is the closed densely defined linear map of X into the Hilbert space H of
Lemma 35 , then the closure of AQA - 1 is a bounded normal operator . For each
bounded Borel function g on the plane let Š ( g ) denote the closure of AS ( 9 ) A -
1 .
If A is the closed densely defined linear map of X into the Hilbert space H of
Lemma 35 , then the closure of AQA - 1 is a bounded normal operator . For each
bounded Borel function g on the plane let Š ( g ) denote the closure of AS ( 9 ) A -
1 .
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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 |