## Linear Operators, Part 2 |

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Results 1-3 of 21

Page 1243

6 ) when the elements of the

1 THEOREM . ( Stone ) If { U ( t ) , t 2 0 } is a strongly continuous

unitary operators in Hilbert space , then there is a unique ( possibly unbounded )

...

6 ) when the elements of the

**semi**-**group**are unitary operators on Hilbert space .1 THEOREM . ( Stone ) If { U ( t ) , t 2 0 } is a strongly continuous

**semi**-**group**ofunitary operators in Hilbert space , then there is a unique ( possibly unbounded )

...

Page 1258

8 ( Cooper ) The infinitesimal generator of a strongly continuous

( t ) } of partially isometric operators whose initial domains are H is of the form iT ,

where T is a maximal symmetric operator with positive deficiency ...

8 ( Cooper ) The infinitesimal generator of a strongly continuous

**semi**-**group**{ V( t ) } of partially isometric operators whose initial domains are H is of the form iT ,

where T is a maximal symmetric operator with positive deficiency ...

Page 1852

An inversion formula for Laplace transforms and

. Ann . of Math . ( 2 ) 59 , 325 – 356 ( 1954 ) . The adjoint

Math . 5 , 269 - 283 ( 1955 ) . A decomposition of additive set functions . Bull .

An inversion formula for Laplace transforms and

**semi**-**groups**of linear operators. Ann . of Math . ( 2 ) 59 , 325 – 356 ( 1954 ) . The adjoint

**semi**-**group**. Pacific J .Math . 5 , 269 - 283 ( 1955 ) . A decomposition of additive set functions . Bull .

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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 give 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