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 1990
for some E - measurable and essentially bounded complex valued function â on
RN Before illustrating the results of the preceding section , we shall examine the
structure of these operators in A and in particular show that many of the ...
for some E - measurable and essentially bounded complex valued function â on
RN Before illustrating the results of the preceding section , we shall examine the
structure of these operators in A and in particular show that many of the ...
Page 2092
The single valued extension property . The example of an operator which does
not have the single valued extension property that is given in Section 2 is due to
S . Kakutani ( see Dunford [ 18 ] ) . Kesel ' man ( 1 ) gave necessary conditions for
...
The single valued extension property . The example of an operator which does
not have the single valued extension property that is given in Section 2 is due to
S . Kakutani ( see Dunford [ 18 ] ) . Kesel ' man ( 1 ) gave necessary conditions for
...
Page 2409
( a ) Instead of considering , as above , the space L2 ( D ) of complex valued
Lebesgue measurable functions defined in D and satisfying ( 7 ) , we may let X
be an arbitrary complex B - space , and can consider the space L ( D , X ) of X -
valued ...
( a ) Instead of considering , as above , the space L2 ( D ) of complex valued
Lebesgue measurable functions defined in D and satisfying ( 7 ) , we may let X
be an arbitrary complex B - space , and can consider the space L ( D , X ) of X -
valued ...
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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