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

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Page 1094

Then by Minkowski's

Then by Minkowski's

**inequality**, +1 - 1 / p 1 / o ( Ž 14--179 ) { 4.17 . ) " + { ( Taya ) . " IM2 + ( ) ? ( 12 S Σ + ( T Σ n + + 1 n = 0 n = 0 n = 0 = \ Tilo + 1T2 . P In the same way ( mm ) ) " 17ıl + | Talv Σ ...Page 1105

We now pause to sharpen another of the

We now pause to sharpen another of the

**inequalities**of Lemma 9 . ... the continuity of the norm function which follows from the triangle**inequality**of Lemma 14 ( d ) , and by Lemma 11 , it follows that we may without loss of generality ...Page 1774

The above

The above

**inequality**, known as the Schwarz**inequality**, will be proved first . It follows from the postulates for Ý that the Schwarz**inequality**is valid if either x or y is zero . Hence suppose that # # 0 #y . For an arbitrary complex ...### 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