## Linear Operators: Spectral theory |

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Page 931

The theorem of Wermer [ 4 ] cited in the preceding paragraph gives a condition

under which the

again normal . Wermer [ 5 ] studied the

M ...

The theorem of Wermer [ 4 ] cited in the preceding paragraph gives a condition

under which the

**restriction**of a normal operator to every invariant subspace isagain normal . Wermer [ 5 ] studied the

**restriction**of an operator T to a subspaceM ...

Page 1218

... function f on R and every ε > 0 there is a Borel set o in R with u ( o ) < € and

such that the

the ...

... function f on R and every ε > 0 there is a Borel set o in R with u ( o ) < € and

such that the

**restriction**of f to the complement of o is continuous . Proof . If the**restrictions**fo , gd are continuous then so is the**restriction**( af + ßglo n d and thusthe ...

Page 1239

Conversely , let T , be a self adjoint extension of T . Then by Lemma 26 , T , is the

linearly independent boundary conditions B ; ( x ) = 0 , i = 1 , . . . , k , and we ...

Conversely , let T , be a self adjoint extension of T . Then by Lemma 26 , T , is the

**restriction**of T * to a subspace W of D ( T * ) determined by a symmetric family oflinearly independent boundary conditions B ; ( x ) = 0 , i = 1 , . . . , k , and we ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive 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 differential equations 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 multiplicity neighborhood norm obtained partial positive preceding present problem Proc 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