## Linear Operators, Part 2 |

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Page 1223

In the theory of bounded

T is everywhere defined and

situation is quite different. Consider, as an example, an

In the theory of bounded

**operators**, we have only to verify**symmetry**(T* Q T), for ifT is everywhere defined and

**symmetric**, then T' = T. But if T is unbounded thesituation is quite different. Consider, as an example, an

**operator**which will be ...Page 1271

frequently-used device, it is appropriate that we give a brief sketch indicating how

the Cayley transform can be used to determine when a

self adjoint extension. Let T be a

frequently-used device, it is appropriate that we give a brief sketch indicating how

the Cayley transform can be used to determine when a

**symmetric operator**has aself adjoint extension. Let T be a

**symmetric operator**with domain 'D(T) dense ...Page 1272

It may be proved that SD, and SD_ are the same manifolds introduced in

Definition 4-.9, and that an isometric operator V ... If T is a

dense domain, then it has proper symmetric extensions provided both of its

deficiency ...

It may be proved that SD, and SD_ are the same manifolds introduced in

Definition 4-.9, and that an isometric operator V ... If T is a

**symmetric operator**withdense domain, then it has proper symmetric extensions provided both of its

deficiency ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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