## Linear Operators: Spectral theory |

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Page 866

Since G is open ( Lemma 3 ) the closure F C G ' and hence + X. The continuity of the algebraic operations shows that I satisfies the other requirements for an

Since G is open ( Lemma 3 ) the closure F C G ' and hence + X. The continuity of the algebraic operations shows that I satisfies the other requirements for an

**ideal**. Thus the closure of a right , left , or two - sided**ideal**is also a ...Page 868

Commutative B - Algebras In case X is a commutative B - algebra every

Commutative B - Algebras In case X is a commutative B - algebra every

**ideal**I is two - sided and the quotient algebra X / I is again a commutative algebra . It will be a B - algebra if I is closed ( 1.13 ) .Page 1162

For our purposes we define a closed

For our purposes we define a closed

**ideal**to be primary if it is contained in precisely one regular maximal**ideal**. Theorem 1.16 may be interpreted as saying that every primary**ideal**in Ly ( R ) is a regular maximal**ideal**.### 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 |

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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