## Linear Operators: Spectral theory |

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Page 1061

Thus \ Htlo sup Is to / ( x ) g ( x ) dx = Kellpy by Theorem IV.8.1 , the Hahn - Banach theorem ( II.3.14 ) and Hölder's

Thus \ Htlo sup Is to / ( x ) g ( x ) dx = Kellpy by Theorem IV.8.1 , the Hahn - Banach theorem ( II.3.14 ) and Hölder's

**inequality**, and the theorem is proved for all p , 1 < p < 0. Q.E.D. Having proved the basic**inequality**of M. Riesz ...Page 1094

Then by Minkowski's

Then by Minkowski's

**inequality**, Š . luant ( 7 ) " ) " = { 3 \ nt ( 7,3 } " + n = 0 5 T1 , + \ Telp : In the same way Šest ) ) " " 17 , 1 + 741 Thus the first assertion of ( b ) follows on addition . The assertion of ( b ) , for the ...Page 1105

We now pause to sharpen another of the

We now pause to sharpen another of the

**inequalities**of Lemma 9 . ... the continuity of the norm function which follows from the triangle**inequality**of Lemma 14 ( d ) , and by Lemma 11 , it follows that we may without loss of generality ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk 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