Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 84
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 [ 8 ; +1 , mi + 1 ] , consider the two functions -f ( t ) and f1 ( t ) + f ( 28 ; + 1 − t ) ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the desired ...
... result . On the interval [ 8 ; +1 , mi + 1 ] , consider the two functions -f ( t ) and f1 ( t ) + f ( 28 ; + 1 − t ) ... 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
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero