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

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Page 866

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

Since G is open ( Lemma 3 ) the closure I Ç G ' and hence I + X. The continuity of the algebraic operations shows that 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 a In case X is a commutative B - algebra every

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

**ideal**I is two - sided and the quotient algebra X3 is again a commutative algebra . It will be a B - algebra if I is closed ( 1.13 ) . It is readily seen that every ...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 4.16 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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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 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 uniformly unique unit unitary vanishes vector zero