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 1977
The preceding theorem shows that the operator valued measure E ( 0 ; A ) given by equation ( ii ) is a countably additive spectral measure in HP defined on the Borel sets B in the complex plane .
The preceding theorem shows that the operator valued measure E ( 0 ; A ) given by equation ( ii ) is a countably additive spectral measure in HP defined on the Borel sets B in the complex plane .
Page 1983
Then A is a spectral operator of scalar type . Proof . The argument of the preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero ...
Then A is a spectral operator of scalar type . Proof . The argument of the preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero ...
Page 2082
Letting Ø and Y be operators defined on Ll ( 01 , M ) and L. ( 01 , ) as in the preceding exercise , show that is a one - to - one and bicontinuous mapping of the non - separable space L. ( 01 , ( ) onto a closed separable subspace sp ...
Letting Ø and Y be operators defined on Ll ( 01 , M ) and L. ( 01 , ) as in the preceding exercise , show that is a one - to - one and bicontinuous mapping of the non - separable space L. ( 01 , ( ) onto a closed separable subspace sp ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 other sections not shown
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