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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Results 1-3 of 81
Page 2162
Thus , in view of Theorem 4 . 5 , to prove the present theorem it suffices to show
that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if
the points regular relative to T are dense on to . Thus Lemmas 12 , 13 , 14 give ...
Thus , in view of Theorem 4 . 5 , to prove the present theorem it suffices to show
that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if
the points regular relative to T are dense on to . Thus Lemmas 12 , 13 , 14 give ...
Page 2248
21 THEOREM . Let T be a spectral operator , and E its resolution of identity . Let f
be a function analytic in a domain U which , when taken together with a finite
number of exceptional points p , includes a neighborhood of o ( T ) and a ...
21 THEOREM . Let T be a spectral operator , and E its resolution of identity . Let f
be a function analytic in a domain U which , when taken together with a finite
number of exceptional points p , includes a neighborhood of o ( T ) and a ...
Page 2283
32 THEOREM . Let B be a complete Boolean algebra of projections in a Banach
space X and let B * be the Boolean algebra of adjoints in B * . Then a projection E
in B has finite uniform multiplicity n if and only if its adjoint E * in B * has finite ...
32 THEOREM . Let B be a complete Boolean algebra of projections in a Banach
space X and let B * be the Boolean algebra of adjoints in B * . Then a projection E
in B has finite uniform multiplicity n if and only if its adjoint E * in B * has finite ...
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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 |