## Linear Operators: Spectral theory |

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Page 1070

symbol Ke for a

same way that there exists another

du < Kos, 2.(o)"u(do). Since by Theorem 11 there exists a

Ko ...

symbol Ke for a

**constant**depending only on e and Q1). We may conclude in thesame way that there exists another

**constant**K, such that (3) s.s, visu)–(K, v.)(u)"du < Kos, 2.(o)"u(do). Since by Theorem 11 there exists a

**constant**K, such that |Ko ...

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and what we shall prove is that for some

(R, X, A). Since it is clear that X* = 2 x 2, what will be proved then, is that (i) Ž(*)(E)

= c(2 × 2)(E), E e X(2), for some

and what we shall prove is that for some

**constant**c, (R(*), X3), 2%)) = c(R, X, A)x(R, X, A). Since it is clear that X* = 2 x 2, what will be proved then, is that (i) Ž(*)(E)

= c(2 × 2)(E), E e X(2), for some

**constant**c independent of E. This condition (i), ...Page 1176

Subtracting a suitable

without loss of generality that k,(– o) = 0 ... here we have used the uniform

boundedness of the functions k, and of their variations to conclude that the

Subtracting a suitable

**constant**c, from each of the functions k, we may supposewithout loss of generality that k,(– o) = 0 ... here we have used the uniform

boundedness of the functions k, and of their variations to conclude that the

**constants**c, ...### 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 |

### Common terms and phrases

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