## Linear Operators: Spectral theory |

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Page 1162

is isomorphic with the complex field, and it turns out that the regular maximal

ideals of L1(R) are in one-to-one correspondence with the points of .40, i.e., with

all the maximal ideals of the algebra

is isomorphic with the complex field, and it turns out that the regular maximal

ideals of L1(R) are in one-to-one correspondence with the points of .40, i.e., with

all the maximal ideals of the algebra

**obtained**by adjoining an identity to L1(R) ...Page 1318

Suppose that the homogeneous system

non-trivial solution a' (c), B}(c), and let Kos.) be the function (of the variable s)

Suppose that the homogeneous system

**obtained**from equations [1] and [2] has anon-trivial solution a' (c), B}(c), and let Kos.) be the function (of the variable s)

**obtained**by substituting 2% and Bo for 2, and p, in [f]. The function Ko is ...Page 1327

If T is a self adjoint operator

boundary conditions, a further simplification can be

solutions of the equation (r”—7)0 = 0 are complex conjugates of the solutions of ...

If T is a self adjoint operator

**obtained**from 1 by imposing a real symmetric set ofboundary conditions, a further simplification can be

**obtained**by noticing that thesolutions of the equation (r”—7)0 = 0 are complex conjugates of the solutions of ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### 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