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 91
Page 1967
If a B * - subalgebra X of a B * - algebra Y has the same unit e as y , then an
element in X with an inverse in Y has this inverse also in X . PROOF . We first
show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee * ) * = e * *
e ...
If a B * - subalgebra X of a B * - algebra Y has the same unit e as y , then an
element in X with an inverse in Y has this inverse also in X . PROOF . We first
show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee * ) * = e * *
e ...
Page 2108
We shall say that an element a e A is scalar ( although Schaefer [ 10 ; p . 143 ]
used ... The elements in the range of va are , in a natural sense , “ functions of a ”
and the mapping g + g ( a ) = valg ) is an operational calculus for a . We say that a
...
We shall say that an element a e A is scalar ( although Schaefer [ 10 ; p . 143 ]
used ... The elements in the range of va are , in a natural sense , “ functions of a ”
and the mapping g + g ( a ) = valg ) is an operational calculus for a . We say that a
...
Page 2215
is fundamental in X . Then a bounded operator is in the weakly closed operator
algebra generated by B if and only if it commutes with every element of B .
PROOF . It is clear that every element in the weakly closed operator algebra
generated ...
is fundamental in X . Then a bounded operator is in the weakly closed operator
algebra generated by B if and only if it commutes with every element of B .
PROOF . It is clear that every element in the weakly closed operator algebra
generated ...
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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 |