## Linear Operators: Spectral theory |

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Page 1207

It is clear from Zorn's lemma that there is a maximal set A in S) for which the

spaces \,, a e A, are

that no r + 0 is

to the ...

It is clear from Zorn's lemma that there is a maximal set A in S) for which the

spaces \,, a e A, are

**orthogonal**. Thus to prove the lemma it suffices to observethat no r + 0 is

**orthogonal**to each of the spaces S). Indeed, if a #0 is**orthogonal**to the ...

Page 1227

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. numbers)

denoted by n, and n_, are called the positive and negative deficiency indices of T,

respectively. 10 LEMMA. (a) Q(T), or, and Q are closed

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. numbers)

denoted by n, and n_, are called the positive and negative deficiency indices of T,

respectively. 10 LEMMA. (a) Q(T), or, and Q are closed

**orthogonal**subspaces ...Page 1777

A set A C S) is called an orthonormal set if each vector in A has norm one and if

every pair of distinct vectors in A is

complete if no non-zero vector is

A set A C S) is called an orthonormal set if each vector in A has norm one and if

every pair of distinct vectors in A is

**orthogonal**. An orthonormal set is said to becomplete if no non-zero vector is

**orthogonal**to every vector in the set, i.e., A is ...### What people are saying - Write a review

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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