## Linear Operators: Spectral theory |

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Page 1469

Thus statement ( a ) follows immediately from the

Thus statement ( a ) follows immediately from the

**preceding**Jemma . To prove statement ( b ) , note that r is finite below 20 , but not below any > 20. Statement ( b ) then follows immediately from the**preceding**lemma .Page 1474

By the remark ( a ) made

By the remark ( a ) made

**preceding**Lemma 41 , 0 < ( 1–42 ) [ 0 ( t , 2. ) ... It follows immediately from the**preceding**lemma that if h1 , h2 € Jm , and h , < a < h2 , then à € Jn . Thus Jn is an interval . Our second assertion follows ...Page 1771

Statement ( i ) follows from the

Statement ( i ) follows from the

**preceding**theorem and Theorem 6.23 . Statement ( ii ) follows from statement ( ii ) of the**preceding**theorem , since a function satisfying the hypotheses of the present statement ( ii ) evidently ( cf.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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additive Akad 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero