## Linear Operators: Spectral theory |

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Page 928

Let A be a bounded self

be a bounded operator which commutes with every operator which commutes

with A. Then there exists a bounded measurable function f such that T = f(A).

Let A be a bounded self

**adjoint operator**on a separable Hilbert space, and let Tbe a bounded operator which commutes with every operator which commutes

with A. Then there exists a bounded measurable function f such that T = f(A).

Page 1191

However, this

that any function g with a continuous first derivative has the property that ( d -( - d

* (i #) i; ; )-(, ; ; ). feo (iii). and thus any such g, even though it fails to vanish at one

...

However, this

**operator**is not self**adjoint**for it is clear from the above equationsthat any function g with a continuous first derivative has the property that ( d -( - d

* (i #) i; ; )-(, ; ; ). feo (iii). and thus any such g, even though it fails to vanish at one

...

Page 1270

The problem of determining whether a given symmetric

theorem may be employed. If the answer to this problem is affirmative, it is

important to ...

The problem of determining whether a given symmetric

**operator**has a self**adjoint**extension is of crucial importance in determining whether the spectraltheorem may be employed. If the answer to this problem is affirmative, it is

important to ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero