Linear Operators: Spectral operators |
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Page 968
... established in Theorem 11 , is a homeomorphism of M。 onto R. PROOF . We first show that the mapping m → h , is continuous . Let mo be an arbitrary point in Mo , 0 < ɛ < 1 , and let N ( hm , K , ε ) , то be a neighborhood of hm . By IV ...
... established in Theorem 11 , is a homeomorphism of M。 onto R. PROOF . We first show that the mapping m → h , is continuous . Let mo be an arbitrary point in Mo , 0 < ɛ < 1 , and let N ( hm , K , ε ) , то be a neighborhood of hm . By IV ...
Page 1193
... established in Lemma 2 . Consider the homeomorphism μh ( 2 ) of the compact complex sphere which is given by the equation μ = ( i - 2 ) -1 . We shall show first that h maps σ ( T ) { ∞ } onto σ ( R ( i ; T ) ) . Let λ i be a point in p ...
... established in Lemma 2 . Consider the homeomorphism μh ( 2 ) of the compact complex sphere which is given by the equation μ = ( i - 2 ) -1 . We shall show first that h maps σ ( T ) { ∞ } onto σ ( R ( i ; T ) ) . Let λ i be a point in p ...
Page 1273
... established by Calkin [ 3 ] . ) - Semi - bounded operators . Von Neumann [ 7 ; p . 103 ] proved that a semi - bounded symmetric operator can be extended to a self adjoint operator with arbitrarily small change in the bound . He ...
... established by Calkin [ 3 ] . ) - Semi - bounded operators . Von Neumann [ 7 ; p . 103 ] proved that a semi - bounded symmetric operator can be extended to a self adjoint operator with arbitrarily small change in the bound . He ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology unique unitary vanishes vector zero