## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 878

Clearly the requirement that x and g ( u ) = u be

Clearly the requirement that x and g ( u ) = u be

**corresponding**elements determines the * -isomorphism uniquely and we are thus led to the following definition . a n nm 1 12 DEFINITION . Let x be an element of a commutative B * -algebra ...Page 942

Thus every eigenfunction of T , which

Thus every eigenfunction of T , which

**corresponds**to a non - zero eigenvalue is a finite dimensional continuous function . Hence N is orthogonal to every eigenfunction of T , except to those**corresponding**to a = 0.Page 1729

It should be evident from this last formula that much as in the

It should be evident from this last formula that much as in the

**corresponding**case of the space 0 ( C ) , we may regard any point x = [ xı , y ] for which 0 < x ; < 2n as belonging , in a suitable sense , to the interior of C ; that is ...### What people are saying - Write a review

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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