## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 93

Page 2174

In a Hilbert space the condition that lett | M for all te R implies that T is equivalent to a self adjoint operator and

In a Hilbert space the condition that lett | M for all te R implies that T is equivalent to a self adjoint operator and

**hence**is a scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded ...Page 2312

If T * y * = 0 , then y * y = y * T2 = ( T * y * ) z = 0 for all y = Tz in the range of T , and

If T * y * = 0 , then y * y = y * T2 = ( T * y * ) z = 0 for all y = Tz in the range of T , and

**hence**for all y in the closure of the range of T. On the other hand , if y is not in the closure of the range of T , then by the Hahn ...Page 2357

then it is clear that L is a bounded operator and that ( S – XI ) -v = ( T - XI ) - L.

then it is clear that L is a bounded operator and that ( S – XI ) -v = ( T - XI ) - L.

**Hence**( P + N ) ( S – XI ) -v = P ( S – XI ) - " + N ( S – 21 ) - " = P ( T - XI ) -L + N ( S - 1 ) - " is a bounded operator which is compact if P ...### 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