## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 87

Page 2160

It will next be

It will next be

**shown**that the vector x Y is in the closure of the manifold ( 1.1 -T ' ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that x * ( x - y ) = 0 for every linear function 2 * which vanishes on ...Page 2226

... then X has an equivalent norm such that the functionals given by Lemma 3.12 can be expressed by means of a semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ] has

... then X has an equivalent norm such that the functionals given by Lemma 3.12 can be expressed by means of a semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ] has

**shown**that in a complete metrizable locally convex space ...Page 2266

It will be

It will be

**shown**that 6 is a dense o - ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set 8 is a dense o - ideal in B. A projection belongs to C if and only if ...### 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