## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 88

Page 2149

If the resolvent set is

If the resolvent set is

**dense**, then any two analytic , or even continuous , extensions of R ( ; T ' ) x must coincide on their common domain of continuity ...Page 2156

are both

are both

**dense**in X. Since M , is**dense**in X , the manifold ( 141 – T ) NM , + { x | ( I – T ' ) ^ x = 0 } is**dense**in X , so that ( 1,1 – T ) ^ ( 1,1 – T ) ...Page 2159

To see that it is

To see that it is

**dense**, let y be a closed subarc of I " , having positive length and let γη = { λολο εγ , λ – λο ] * | R ( λ ; Τ ' ) $ 1 , λο # λε Διο ...### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

### Other editions - View all

### Common terms and phrases

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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit 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