Linear Operators: Spectral operators |
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Page 2403
We then use this inequality to apply Theorem 1 in an illustrative but somewhat
artificial setting , essentially to multiplication ... A first application ( Theorem 6 ) is
made in this way , and immediately following upon this we develop a similar but ...
We then use this inequality to apply Theorem 1 in an illustrative but somewhat
artificial setting , essentially to multiplication ... A first application ( Theorem 6 ) is
made in this way , and immediately following upon this we develop a similar but ...
Page 2413
We may now apply Theorem 1 to conclude that there exists a positive constant ε
depending only on P , D , and c , such that the operators T and T + ( A ) are
similar whenever | | A | | < £ . Q . E . D . Theorem 1 and its corollaries are readily ...
We may now apply Theorem 1 to conclude that there exists a positive constant ε
depending only on P , D , and c , such that the operators T and T + ( A ) are
similar whenever | | A | | < £ . Q . E . D . Theorem 1 and its corollaries are readily ...
Page 2434
Applying Theorem 8 and Corollary 9 , the present theorem follows at once . Q . E .
D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .
16 ) , we may apply Theorem 21 to analyze a variety of operators . The following
...
Applying Theorem 8 and Corollary 9 , the present theorem follows at once . Q . E .
D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .
16 ) , we may apply Theorem 21 to analyze a variety of operators . The following
...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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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 defined Definition denote dense determined differential operator discrete 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 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