## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 67

Page 1120

Throughout the present section , we

Throughout the present section , we

**assume**for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces .Page 1594

( 6 ) In the interval ( a , b ) ( b < 0 )

( 6 ) In the interval ( a , b ) ( b < 0 )

**assume**( a ) the function g is non - negative and piecewise continuous in the interval [ 0 , 00 ) , ( b ) the solutions of the differential equation da f ( t ) + g ( t ) / ( t ) = 0 ( 0 < t < 00 ) ...Page 1595

( 10 )

( 10 )

**Assuming**( a ) through ( e ) of ( 6 ) , and letting the function Z be as in ( f ) , if lim inf Z ( t ) ... P ( s ) -ds and**assume**that lim inf 2 ( t ) = K. Then the essential spectrum of 1 is contained in the half - line ( K ...### 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

### Other editions - View all

### 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