Linear Operators, Part 2 |
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Page 1115
... resolvent of T satisfy the inequality | R ( λ ; T ) | = O ( | 2 | ~~ ) as λ → 0 along any of the arcs y . Then the subspace sp ( T ) contains the subspace TN . The very minor adaptations of the proof of Theorem 6.29 needed to yield the ...
... resolvent of T satisfy the inequality | R ( λ ; T ) | = O ( | 2 | ~~ ) as λ → 0 along any of the arcs y . Then the subspace sp ( T ) contains the subspace TN . The very minor adaptations of the proof of Theorem 6.29 needed to yield the ...
Page 1144
... resolvent of T satisfies the inequality | R ( 2 ; T ) | = O ( | 2 | -N ) as 20 along any of the arcs 7. Then the subspace sp ( T ) contains the subspace TNS . Similarly , by arguing as in the proofs of Corollary 6.30 and Corollary 6.31 ...
... resolvent of T satisfies the inequality | R ( 2 ; T ) | = O ( | 2 | -N ) as 20 along any of the arcs 7. Then the subspace sp ( T ) contains the subspace TNS . Similarly , by arguing as in the proofs of Corollary 6.30 and Corollary 6.31 ...
Page 1187
... resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( 2 ; T ) will be used for the resolvent ...
... resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( 2 ; T ) will be used for the resolvent ...
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BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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(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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero