## Linear Operators, Part 2 |

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Page 1297

The first

The first

**norm**is the**norm**of the pair [ 1 , T1 / ] as an element of the graph of T ( T ) . Now Ti ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( T1 ( ) ) is complete in the**norm**\ / lı . Since the two additional ...Page 1431

Thus { gm } converges to zero in the

Thus { gm } converges to zero in the

**norm**of D ( T ( 7 ' ) ) . ( e ) The closure of D ( T. ( ' ) ) in the**norm**of D ( T ( 7 ' ) ) coincides with the closure of D ( T. ( t ' ) ) in the**norm**of D ( Ti ( ) ) .Page 1639

1 + ult ; J , m ) This

1 + ult ; J , m ) This

**norm**makes each of the spaces listed above into a complete F - space . If k < 0o and I is compact , but not otherwise , the spaces C * ( I ) and C ( I ) are B - spaces under a**norm**equivalent to the**norm**displayed ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero