## Linear Operators: Spectral theory |

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Page 905

the spectrum of the bounded normal operator T in § is countable then there is an

y)v> xe§, and, for each x, all but a countable number of the coefficients (x, y) are ...

the spectrum of the bounded normal operator T in § is countable then there is an

**orthonormal**basis B for Sp consisting of eigenvectors of T. Furthermore, « = 2 (*«y)v> xe§, and, for each x, all but a countable number of the coefficients (x, y) are ...

Page 1010

Let {xa, a e A} be a complete

linear operator T is said to be a Hilbert-Schmidt operator in case the quantity ||T||

defined by the equation \\n={i\Tx*\*}i as A is finite. The number ||T|| is sometimes ...

Let {xa, a e A} be a complete

**orthonormal**set in the Hilbert space A boundedlinear operator T is said to be a Hilbert-Schmidt operator in case the quantity ||T||

defined by the equation \\n={i\Tx*\*}i as A is finite. The number ||T|| is sometimes ...

Page 1779

A set A is called an

closed linear manifold in !q contains an

A set A is called an

**orthonormal**basis for the linear manifold 31 in Q if A is an**orthonormal**set contained in 9t and if * = 2 (*» v)y> # e 5R. 12 Theorem. Everyclosed linear manifold in !q contains an

**orthonormal**basis for itself. Proof.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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