## Linear Operators: Spectral theory |

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Since there is a

have |T| < |T|*+e and hence |T| < |T||. Q.E.D. 3 CorollARY. If T is in HS and {rx, & e

A} is any

Since there is a

**complete**orthonormal set containing the element ro we clearlyhave |T| < |T|*+e and hence |T| < |T||. Q.E.D. 3 CorollARY. If T is in HS and {rx, & e

A} is any

**complete**orthonormal set in S), then |T|| = { X (Tr., ra)*}}. 2, 6 e A PRoof.Page 1147

CoRoLLARy: If G is a compact topological group satisfying the second axiom of

countability, and G is not a finite set, then any

G is countable. A

CoRoLLARy: If G is a compact topological group satisfying the second axiom of

countability, and G is not a finite set, then any

**complete**set of representations ofG is countable. A

**complete**set of representations of a finite group is finite.Page 1903

definition, II.3.25 (67) in reflexive spaces, II.3.28 (68) Complement,

orthocomplement, IV.4.3 (249) orthogonal, II.4.17 (72) and projections, (553–554)

of a set, (2) Complemented lattice, (43)

definition, II.3.25 (67) in reflexive spaces, II.3.28 (68) Complement,

orthocomplement, IV.4.3 (249) orthogonal, II.4.17 (72) and projections, (553–554)

of a set, (2) Complemented lattice, (43)

**Complete**and o-**complete**lattice, (43)**Complete**...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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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