## Linear Operators: Spectral theory |

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Results 1-3 of 90

Page 875

2 Lemma. The algebra B(£>) of all bounded linear operators in Hilbert space ,£)

in which the operation * of involution is defined by equation (i) is a B* '-algebra.

Our chief objective in this section is to characterize commutative

2 Lemma. The algebra B(£>) of all bounded linear operators in Hilbert space ,£)

in which the operation * of involution is defined by equation (i) is a B* '-algebra.

Our chief objective in this section is to characterize commutative

**B*-algebras**.Page 877

A commutative

equivalent to the

Corollary. Let 7) be a B*-subalgebra of the commutative

suppose that X and ...

A commutative

**B*-algebra**of operators in Hilbert space is isometrically ^-equivalent to the

**B*-algebra**of all continuous functions on its spectrum. 10Corollary. Let 7) be a B*-subalgebra of the commutative

**B*-algebra**X andsuppose that X and ...

Page 884

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the results given in Section 1 are due. B- and

Section 2 are due to Gelfand [1]. The fundamental Theorem 8.7 was proved by ...

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the results given in Section 1 are due. B- and

**B*-algebras**. The results ofSection 2 are due to Gelfand [1]. The fundamental Theorem 8.7 was proved by ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

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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