## Linear Operators: Spectral theory |

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Page 875

It will also be shown that this

It will also be shown that this

**isomorphism**is a * -**isomorphism**, i.e. , one preserving the operation of involution . This basic result , which is due to Gelfand and Naïmark , will find many applications in the next two chapters .Page 878

a one * -

a one * -

**isomorphism**of B * ( x ) onto C ( 0 ( x ) ) into another one . ... 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 ...Page 1355

2 = = Ly ( u , e ; ) ) that V is an isometric

2 = = Ly ( u , e ; ) ) that V is an isometric

**isomorphism**of E ( 1 ) L2 ( 1 ) onto L ( 1 , { P is } ) and that A is an isometric**isomorphism**of L2 ( 4 , { Pii } ) onto the subspace -L ( u , Ae ; ) of X - Ly ( u , e ; ) .### What people are saying - Write a review

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### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume 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 domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero