Linear Operators: Spectral theory |
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Page 1267
... map u → u ( T ) is an order - preserving linear map of the real algebra o into the real algebra ( S ) , and that ( Hint : Use Exercise 32. ) 0 u ( T ) ≤ max | u ( λ ) . 251 ( b ) Extend the homomorphism of part ( a ) to an order ...
... map u → u ( T ) is an order - preserving linear map of the real algebra o into the real algebra ( S ) , and that ( Hint : Use Exercise 32. ) 0 u ( T ) ≤ max | u ( λ ) . 251 ( b ) Extend the homomorphism of part ( a ) to an order ...
Page 1299
... linear mapping of the space of boundary values for ' at a onto the space of ... linear operator defined by the equation In the formula ( S1f ) ( t ) = h ( t ) f ... map from M ' to M. It will be shown that Ø1 is one - to - one and that Ø1 ...
... linear mapping of the space of boundary values for ' at a onto the space of ... linear operator defined by the equation In the formula ( S1f ) ( t ) = h ( t ) f ... map from M ' to M. It will be shown that Ø1 is one - to - one and that Ø1 ...
Page 1682
... linear map defined by equation ( iv ) , and let [ T ,,, be its norm as a mapping from L ( E " ) into L ( E ” ) . We have seen that the norms | T | 1 ,, and T , ∞ where p - 1 + q - 1 -1 1 , are both finite . Consider the points u = ( q ...
... linear map defined by equation ( iv ) , and let [ T ,,, be its norm as a mapping from L ( E " ) into L ( E ” ) . We have seen that the norms | T | 1 ,, and T , ∞ where p - 1 + q - 1 -1 1 , are both finite . Consider the points u = ( q ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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Common terms and phrases
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