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

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Page 906

A bounded operator T in Hilbert space w is called

A bounded operator T in Hilbert space w is called

**unitary**if TT * = T * T = 1 ; it is called self adjoint , symmetric * or Hermitian if T = T * ; positive if it is self adjoint and if ( Tx , x ) 20 for every x in H ; and positive ...Page 931

Applications are made to the restrictions of normal and

Applications are made to the restrictions of normal and

**unitary**operators . Halmos , Lumer , and Schäffer ( 1 ) proved that the restriction of a normal operator may possess an inverse but not a square root ( see also Halmos and Lumer ...Page 1146

0 Rn , and say that R is the direct sum of R , ... , Rn . The following theorem is easily proved by induction in case R is

0 Rn , and say that R is the direct sum of R , ... , Rn . The following theorem is easily proved by induction in case R is

**unitary**, and thus follows in the general case by the theorem stated above . THEOREM .### 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