## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 69

Page 2403

We then use this inequality to

artificial setting , essentially to multiplication ... A first

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 somewhatartificial setting , essentially to multiplication ... A first

**application**( Theorem 6 ) ismade in this way , and immediately following upon this we develop a similar but ...

Page 2413

We may now

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 εdepending 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

D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .

16 ) , we may

...

**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...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete 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 Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero