## Linear Operators, Part 2 |

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Page 1188

The Hilbert space adjoint or simply the adjoint T * is

The Hilbert space adjoint or simply the adjoint T * is

**defined**on D ( T * ) by the ... In this**definition**the domain D ( T ) is required to be dense in ý in ...Page 1196

The formal

The formal

**definition**is as follows . ... Then the operator f ( T ) is**defined**by the equations D ( / ( T ) ) = { x \ lim 1m ( T ) x exists } n where ( 2 ) ...Page 1548

extensions of S and Ŝ respectively , and let an ( T ) and 2n ( ft ) be the numbers

extensions of S and Ŝ respectively , and let an ( T ) and 2n ( ft ) be the numbers

**defined**for the self adjoint operators T and Î as in Exercise D2 .### 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