## Linear Operators: Spectral operators |

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Page 860

A B-

a B-

”, (ry)* = yor” (x,y)* = &r”, (r”)* = r. All of the examples mentioned above, with the ...

A B-

**algebra**3 is commutative in case ary = y:z for all a and y in 3. An involution ina B-

**algebra**& is a mapping r → r* of 3 into itself with the properties (r-i-y)* = a ++y”, (ry)* = yor” (x,y)* = &r”, (r”)* = r. All of the examples mentioned above, with the ...

Page 875

The

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

objective in this section is to characterize commutative B*-

shown ...

The

**algebra**B(S)) of all bounded linear operators in Hilbert space X) in which theoperation * of involution is defined by equation (i) is a B"-

**algebra**. Our chiefobjective in this section is to characterize commutative B*-

**algebras**. It will beshown ...

Page 979

be based upon two closely related commutative

Hilbert space L2(R). One of these

preceding section, we have met before. For convenience, its definition and some

of its ...

be based upon two closely related commutative

**algebras**of operators in theHilbert space L2(R). One of these

**algebras**, namely the**algebra**QI of thepreceding section, we have met before. For convenience, its definition and some

of its ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

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adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero