## Linear Operators, Volume 2 |

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Page 922

**topology**, i.e. , T , & → Tx for every x in the space upon which the operators T , T , 2 , ... , are defined . 1 LEMMA . Let S , T , S. , T. , n 2 1 be bounded linear operators in Hilbert space with Sn → S , T , → T in the strong ...Page 1420

( a ' ) The

( a ' ) The

**topology**of the Hilbert space D ( T1 ( T ) ) is the same as its relative**topology**as a subspace of the Hilbert space D ( T2 ( t + 7 ' ) ) . Indeed , let { { n } be a sequence in D ( Ti ( t ) ) .Page 1921

F ( 1550 ) Subadditive function , definition , ( 618 ) Subbase for a

F ( 1550 ) Subadditive function , definition , ( 618 ) Subbase for a

**topology**, 1.4.6 ( 10 ) criterion for , 1.4.8 ( 11 ) Subspace , of a linear space , ( 36 ) . ( See also Manifold ) Summability , of Fourier series , IV.14.34–51 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive adjoint operator 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 derivatives 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