Linear Operators: Spectral theory |
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Page 931
... Hilbert space S can be extended ( in some sense ) to an operator B in a Hilbert space ft , containing 5 , in such a way that B has properties not possessed by A. = One possible type of extension is the following : if t is a Hilbert space ...
... Hilbert space S can be extended ( in some sense ) to an operator B in a Hilbert space ft , containing 5 , in such a way that B has properties not possessed by A. = One possible type of extension is the following : if t is a Hilbert space ...
Page 1180
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions ƒ with values in any space L , ( 5 ) , H denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions ƒ with values in any space L , ( 5 ) , H denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
Page 1262
... Hilbert space with 0≤ASI be given . Then there exists a Hilbert space 125 , and an orthogonal projection Q in such that Ax = PQx , x = H , P denoting the orthogonal projection of 1 on H. 29 Let { T } be a sequence of bounded operators in ...
... Hilbert space with 0≤ASI be given . Then there exists a Hilbert space 125 , and an orthogonal projection Q in such that Ax = PQx , x = H , P denoting the orthogonal projection of 1 on H. 29 Let { T } be a sequence of bounded operators in ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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