## Linear Operators: Spectral theory |

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Page 1358

i, j=1 J e It

equation [*] holds for all f in L2(I). Q.E.D. 15 CoRoll ARY. Let T, A, and {p,} be

defined as in Theorem 14. The complement of q(T) in A is the largest open subset

eo of ...

i, j=1 J e It

**follows from Theorem**IV.8.l. that [s, K.G. . )*ds]'s M(j), tes, and thatequation [*] holds for all f in L2(I). Q.E.D. 15 CoRoll ARY. Let T, A, and {p,} be

defined as in Theorem 14. The complement of q(T) in A is the largest open subset

eo of ...

Page 1379

{6,6} is the matrix measure of

determined for each e C N. Since A is the union of a sequence of neighborhoods

of the same type as N, the uniqueness of {6,3

{6,6} is the matrix measure of

**Theorem**23, the values 6,(e) are uniquelydetermined for each e C N. Since A is the union of a sequence of neighborhoods

of the same type as N, the uniqueness of {6,3

**follows**immediately. Q.E.D. 27**THEOREM**.Page 1381

By the remark following Definition 2.29, the two linear functionals f – f(0) and f => f

(1) form a complete set of boundary ... Since [0,1] is a closed interval, it

By the remark following Definition 2.29, the two linear functionals f – f(0) and f => f

(1) form a complete set of boundary ... Since [0,1] is a closed interval, it

**follows****from Theorems**4.1 and 4.2 that the spectrum of To consists entirely of isolated ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero