## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 81

Page 1223

Consider , as an example , an operator which will be studied in greater detail in

the next chapter : the differential operator iD = idd / dt ) in the space L2 ( 0 , 1 ) .

How are we to choose its

the ...

Consider , as an example , an operator which will be studied in greater detail in

the next chapter : the differential operator iD = idd / dt ) in the space L2 ( 0 , 1 ) .

How are we to choose its

**domain**? A natural first guess is to choose as**domain**the ...

Page 1249

Thus PP * is a projection whose range is N = PM , the final

complete the proof it will suffice to show that P * P is a projection if P is a partial

isometry . Let x , v EM , the initial

Pv12 ...

Thus PP * is a projection whose range is N = PM , the final

**domain**of P . Tocomplete the proof it will suffice to show that P * P is a projection if P is a partial

isometry . Let x , v EM , the initial

**domain**of P . Then the identity \ x + 012 = \ Px +Pv12 ...

Page 1669

44 DEFINITION . Let I , be a

14 → 1 , be a mapping of Iį into 1 , such that ( a ) M - C is a compact subset of I ,

whenever C is a compact subset of 12 ; ( b ) ( M ( : ) ) ; E Co ( 11 ) , j = 1 , . . . , ng .

44 DEFINITION . Let I , be a

**domain**in Eại , and let I , be a**domain**in En2 . Let M :14 → 1 , be a mapping of Iį into 1 , such that ( a ) M - C is a compact subset of I ,

whenever C is a compact subset of 12 ; ( b ) ( M ( : ) ) ; E Co ( 11 ) , j = 1 , . . . , ng .

### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

39 other sections not shown

### Other editions - View all

### Common terms and phrases

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