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 2137
Even though ( A ) is taken as a standing assumption throughout this section , it
will be indicated parenthetically in the statement of each lemma in the proof of
which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are
vectors in ...
Even though ( A ) is taken as a standing assumption throughout this section , it
will be indicated parenthetically in the statement of each lemma in the proof of
which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are
vectors in ...
Page 2218
Proof . Since a spectral operator of scalar type is clearly in the weakly closed
algebra A generated by the projections in its resolution of the identity , it suffices
to show that every operator in A is a spectral operator of scalar type . This follows
...
Proof . Since a spectral operator of scalar type is clearly in the weakly closed
algebra A generated by the projections in its resolution of the identity , it suffices
to show that every operator in A is a spectral operator of scalar type . This follows
...
Page 2281
The proof is similar to that of Lemma 17 and will be omitted . We turn now to the
representation of E * X * when E * € & * and has finite uniform multiplicity n . The
results are parallel to those in X . The weaker form of completeness enjoyed by B
...
The proof is similar to that of Lemma 17 and will be omitted . We turn now to the
representation of E * X * when E * € & * and has finite uniform multiplicity n . The
results are parallel to those in X . The weaker form of completeness enjoyed by B
...
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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 |