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 1931
Of course it is not clear to begin with that a countably additive resolution of the
identity defined on the Borel sets of the plane is uniquely determined by the
spectral operator T . This is the case , but until it is proved we refer to any such
spectral ...
Of course it is not clear to begin with that a countably additive resolution of the
identity defined on the Borel sets of the plane is uniquely determined by the
spectral operator T . This is the case , but until it is proved we refer to any such
spectral ...
Page 2053
In the examples of Theorems 19 and 21 we did not appeal to the general theory ,
as it was clear from the form of exp tà that T ( t ) o was differentiable for t > 0 and
an arbitrary y in HP . It is even clear that the nth order derivative T ' ( n ) ( t ) exists
...
In the examples of Theorems 19 and 21 we did not appeal to the general theory ,
as it was clear from the form of exp tà that T ( t ) o was differentiable for t > 0 and
an arbitrary y in HP . It is even clear that the nth order derivative T ' ( n ) ( t ) exists
...
Page 2159
Some results in this direction will be found in the next four lemmas . 11 LEMMA (
G ) . The union of all intervals of constancy relative to T is an open set dense in I .
. PROOF . It is clear that the union of intervals of constancy is open . To see that ...
Some results in this direction will be found in the next four lemmas . 11 LEMMA (
G ) . The union of all intervals of constancy relative to T is an open set dense in I .
. PROOF . It is clear that the union of intervals of constancy is open . To see that ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 other sections not shown
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Common terms and phrases
adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector 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 |