## Linear Operators: Spectral theory |

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Page 875

It will be

It will be

**shown**that the homomorphism x + x ( • ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 1 ) of all continuous functions on the structure space 1 of X is an isometric isomorphism of X onto all of C ( 1 ) ...Page 981

If H ( T ( 1 ) ) does not Q. f vanish identically for f in L1 ( R ) then , as was

If H ( T ( 1 ) ) does not Q. f vanish identically for f in L1 ( R ) then , as was

**shown**in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H , ( T ( f ) ) = S xH ( x ) } ( x ) dx , feL ( R ) .Page 1161

That spectral synthesis is not possible for all functions in L. was

That spectral synthesis is not possible for all functions in L. was

**shown**by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been**shown**by M. Paul Malliavin that spectral synthesis is not possible for all ...### 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