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

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The theorem of Wermer [ 4 ] cited in the preceding paragraph gives a condition under which the

The theorem of Wermer [ 4 ] cited in the preceding paragraph gives a condition under which the

**restriction**of a normal operator to every invariant subspace is again normal . Wermer ( 5 ) studied the**restriction**of an operator T to a ...Page 1218

If the

If the

**restrictions**flo , g | 8 are continuous then so is the**restriction**( af + Bg ) o n d and ... e and a closed set o contained in e with po - 8 ) < E. Clearly the**restriction**of Xe to the complement of o - S is continuous .Page 1239

Conversely , let T be a self adjoint extension of T. Then by Lemma 26 , T , is the

Conversely , let T be a self adjoint extension of T. Then by Lemma 26 , T , is the

**restriction**of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B : ( x ) = 0 , i = 1 , ...### 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