## Linear Operators, Part 2 |

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Page 860

A B-

a B-

w*+y*, (M./)* = 2/*w* (<w)* = 6w', (w*)* = wAll of the examples mentioned above, ...

A B-

**algebra**I is commutative in case my = ya: for all m and y in I. An involution ina B-

**algebra**PE is a mapping rc —> a:* of I into itself with the properties (w+y)* =w*+y*, (M./)* = 2/*w* (<w)* = 6w', (w*)* = wAll of the examples mentioned above, ...

Page 875

The

the operation "' of involution is defined by equation (i) is a B*-

objective in this section is to characterize commutative B*-algebras. It will be

shown ...

The

**algebra**B(.§)) of all bounded linear operators in Hilbert space Q) in whichthe operation "' of involution is defined by equation (i) is a B*-

**algebra**. Our chiefobjective in this section is to characterize commutative B*-algebras. It will be

shown ...

Page 979

Nelson Dunford, Jacob T. Schwartz. be based upon two closely related

commutative algebras of operators in the Hilbert space L,(R). One of these

algebras, namely the

For convenience ...

Nelson Dunford, Jacob T. Schwartz. be based upon two closely related

commutative algebras of operators in the Hilbert space L,(R). One of these

algebras, namely the

**algebra**2i of the preceding section, we have met before.For convenience ...

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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