Linear Operators: Spectral theory |
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Page 884
... results of this theory we present only a single result , due to von Neu- mann [ 2 ] , in this direction . If A is a collection of bounded linear opera- tors in a Hilbert space H , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
... results of this theory we present only a single result , due to von Neu- mann [ 2 ] , in this direction . If A is a collection of bounded linear opera- tors in a Hilbert space H , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
Page 1419
... result . On the interval [ si + 1 , mi + 1 ] , consider the two functions -f ( t ) and f1 ( t ) = + f ( 28 , + 1 ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the desired ...
... result . On the interval [ si + 1 , mi + 1 ] , consider the two functions -f ( t ) and f1 ( t ) = + f ( 28 , + 1 ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the desired ...
Page 1591
... result similar to Lemma 8 can be found in the joint paper of Krein , Krasnosel'skii and Milman [ 1 ] . Theorem 11 was obtained by Weyl for operators of the second order , and extended by Glazman [ 1 ] . The trick used in Theorem 14 has ...
... result similar to Lemma 8 can be found in the joint paper of Krein , Krasnosel'skii and Milman [ 1 ] . Theorem 11 was obtained by Weyl for operators of the second order , and extended by Glazman [ 1 ] . The trick used in Theorem 14 has ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero