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

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**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 869

Every homomorphism of a

Every homomorphism of a

**commutative**B - algebra into the complex number system is continuous . 3 - LEMMA . Let M be the set of maximal ideals in the**commutative**B - algebra X. Then x ( M ) = 0 ( x ) and sup 2 ( 2 ) | = lim r " ] } { " .Page 882

Show that with the product u * 2 the Banach space M is a

Show that with the product u * 2 the Banach space M is a

**commutative**Banach algebra . 14 If f is in Li ( -0 , 0 ) , and if 2 ( E ) = Sef ( s ) ds show that ( 2 * u ) ( E ) = leds Lot ( s — t ) u ( dt ) , for every u in the space M of ...### 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