## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 77

Page 1027

( a ) Since H is infinite dimensional the origin

( a ) Since H is infinite dimensional the origin

**belongs**to the spectrum of both T and ET . Suppose that 1 # 0**belongs**to the spectrum of T. Since T is compact , Theorem VII.4.5 shows that 2 is an eigenvalue and ...Page 1116

2,2 < oo , E ) ? . i = 1 i = 1 ܕ so that , by Definition 6.1 , B

2,2 < oo , E ) ? . i = 1 i = 1 ܕ so that , by Definition 6.1 , B

**belongs**to the Hilbert - Schmidt class Cz . If we let Aq ; = ri , 1 - p / 2 Pi , then A is plainly self adjoint and A**belongs**to the class Co , where r ( 1 - p / 2 ) = p ...Page 1602

Then the point 2

Then the point 2

**belongs**to the essential spectrum of 7 ( Hartman and Wintner [ 14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let | be a real solution of the equation ( 2-1 ) } = 0 on ( 0 , 0 ) which is not square ...### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

44 other sections not shown

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero