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

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Page 932

An

An

**extension**to B - spaces was given by Sz . - Nagy [ 10 ; p . 114 ) , and similar results for semigroups of contractions are found in Sz . - Nagy ( 8 , 10 ) ( see also Cooper [ 3 ] ) . Sz . - Nagy's original proof depended on the ...Page 947

Each h ; has a unique

Each h ; has a unique

**extension**to a continuous function on S and we denote this**extension**by the same letter . Hence there are neighborhoods U , of $ , and U , of s , such that for sin U1 , \ h ; ( $ 1 ) -h ; ( ) < 0/2 and for sin U2 ...Page 1225

The most general symmetric

The most general symmetric

**extension**T , of T is the restriction of T * to a symmetric subspace D of D ( T * ) which contains D ( T ) . To penetrate further into the problem we must make use of the topology introduced into D ( T * ) by ...### 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 Ly(R 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 unique unit unitary vanishes vector zero