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 t 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 t 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 lo
. Proof . It is clear that the union of intervals of constancy is open . To see that it ...
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 lo
. Proof . It is clear that the union of intervals of constancy is open . To see that it ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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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