## Linear Operators, Part 2 |

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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 _

d (ZE]',g)—(f,'lEg), /6§D(lIt)» and thus any such g, even though it fails to vanish at

...

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 _

d (ZE]',g)—(f,'lEg), /6§D(lIt)» and thus any such g, even though it fails to vanish at

...

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 | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero