## Linear Operators, Part 2 |

### From inside the book

Results 1-3 of 18

Page 1904

... 1V.10.9 (325) Vitali-Hahn-Saks theorem for measures, 111.7.2-4 (158-160)

Weierstrass theorem on analytic functions, (228) Convex combination, V.2.2 (414

). (See also Conve.1' hull,

, ...

... 1V.10.9 (325) Vitali-Hahn-Saks theorem for measures, 111.7.2-4 (158-160)

Weierstrass theorem on analytic functions, (228) Convex combination, V.2.2 (414

). (See also Conve.1' hull,

**Convex set**, Convex space) Convex function, definition, ...

Page 1911

... (88-85) Interior point, 1.4.1 (10) Interior of a set, 1.4.1 (10) Internal point,

definition, V.1.6 (410) Intervals, definitions, (4), ... v.s.4 (440) Krein-Smulian

theorem, on convex closure of a weakly compact set, v.6.4 (484) on I closed

... (88-85) Interior point, 1.4.1 (10) Interior of a set, 1.4.1 (10) Internal point,

definition, V.1.6 (410) Intervals, definitions, (4), ... v.s.4 (440) Krein-Smulian

theorem, on convex closure of a weakly compact set, v.6.4 (484) on I closed

**convex sets**in I' ...Page 1912

inferior (or superior), of a set or sequence of real numbers, (4) ofa sequence of

sets, 111.4-.3 (126) point of a set, 1.4.1 ... in the bounded E topology, v.5.5 (4.2s)

separation of

...

inferior (or superior), of a set or sequence of real numbers, (4) ofa sequence of

sets, 111.4-.3 (126) point of a set, 1.4.1 ... in the bounded E topology, v.5.5 (4.2s)

separation of

**convex sets**in, V.2.1013 (417—4-18) Lower bound for an operator,...

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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