## Linear Operators: Spectral theory |

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Page 1027

Then f(ET) = Ef(T), f(T) = f(T)F, tr(f(T), T) = tr(f(ET), ET), and tr(f(ET), ET) coincides

with the trace of the restriction of the operator ET/(T) to the finite dimensional

PRoof. (a) Since $) is infinite dimensional the origin

both ...

Then f(ET) = Ef(T), f(T) = f(T)F, tr(f(T), T) = tr(f(ET), ET), and tr(f(ET), ET) coincides

with the trace of the restriction of the operator ET/(T) to the finite dimensional

PRoof. (a) Since $) is infinite dimensional the origin

**belongs**to the spectrum ofboth ...

Page 1116

co, i-1 i-1 so that, by Definition 6.1, B

we let Ap, = y; "p, then A is plainly self adjoint and A

where r(1–p/2) = p, i.e., r = p(1–p/2)-1. Thus, by Lemma 9, T = BA

class ...

co, i-1 i-1 so that, by Definition 6.1, B

**belongs**to the Hilbert-Schmidt class Cs. Ifwe let Ap, = y; "p, then A is plainly self adjoint and A

**belongs**to the class C.,where r(1–p/2) = p, i.e., r = p(1–p/2)-1. Thus, by Lemma 9, T = BA

**belongs**to theclass ...

Page 1602

Then the point A

]). (48) Suppose that the function q is bounded below, and let f be a real solution

of the equation (A—t)f = 0 on [0, oo) which is not square-integrable but which ...

Then the point A

**belongs**to the essential spectrum of r (Hartman and Wintner [14]). (48) Suppose that the function q is bounded below, and let f be a real solution

of the equation (A—t)f = 0 on [0, oo) which is not square-integrable but which ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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