## Linear Operators: Spectral theory |

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Page 1019

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. volume of

any n-sided parallelepiped is never larger than the volume of a rectangular

parallelepiped with sides of the same lengths. PRoof. The

for n ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. volume of

any n-sided parallelepiped is never larger than the volume of a rectangular

parallelepiped with sides of the same lengths. PRoof. The

**inequality**is obviousfor n ...

Page 1105

We now pause to sharpen another of the

the paragraph following Lemma 9, the continuity of the norm function which

follows from the triangle

that ...

We now pause to sharpen another of the

**inequalities**of Lemma 9. ... was noted inthe paragraph following Lemma 9, the continuity of the norm function which

follows from the triangle

**inequality**of Lemma 14(d), and by Lemma 11, it followsthat ...

Page 1774

A Hilbert space $) is a complea B-space and |(a, v) = |x||y|, w, ye $). PRoof. The

above

from the postulates for S) that the Schwarz

.

A Hilbert space $) is a complea B-space and |(a, v) = |x||y|, w, ye $). PRoof. The

above

**inequality**, known as the Schwarz**inequality**, will be proved first. It followsfrom the postulates for S) that the Schwarz

**inequality**is valid if either a or y is zero.

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero