## Linear Operators: Spectral operators |

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Page 1100

matrix with the same eigenvalues as A, the statement (3)

inequality str(VD, V"D, w") s |Di, Del. ... Q.E.D. It

preceding

10 that for ...

matrix with the same eigenvalues as A, the statement (3)

**follows**from theinequality str(VD, V"D, w") s |Di, Del. ... Q.E.D. It

**follows**immediately from thepreceding

**lemma**, from**Lemma**9 (d), from the fact that |A| < |A|, and from**Lemma**10 that for ...

Page 1102

The formula e" 4 = det(A) is valid for finite-dimensional matrices, det(A) denoting

the determinant of A. Since the determinant of A is the product of its eigenvalues,

it

The formula e" 4 = det(A) is valid for finite-dimensional matrices, det(A) denoting

the determinant of A. Since the determinant of A is the product of its eigenvalues,

it

**follows**by**Lemma**6(a) that we have d | det(1+zT) = TI 2,(I+2T) = 1 which ...Page 1733

... it

the method of proof of Theorem 2 in the neighborhood of the boundary of a

domain ...

... it

**follows**that A-(fo S-f), is uniformly bounded in A, from which the present**lemma follows**, as has been shown above. Q.E.D.**Lemma**18 enables us to usethe method of proof of Theorem 2 in the neighborhood of the boundary of a

domain ...

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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