Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1092
... finite number N of non - zero eigenvalues , we write λ , ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
... finite number N of non - zero eigenvalues , we write λ , ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
Page 1459
... finite below any finite λ . PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 20 in order to conclude that t is finite below 2. But it was shown in the ...
... finite below any finite λ . PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 20 in order to conclude that t is finite below 2. But it was shown in the ...
Page 1460
... finite below λ , and the leading coefficient of t + t1 never vanishes , t + t1 is finite below λ . Τι PROOF . It is clear that we may suppose without loss of generality that λ = 0. By Corollary 24 ( b ) , Corollary XII.4.13 , and ...
... finite below λ , and the leading coefficient of t + t1 never vanishes , t + t1 is finite below λ . Τι PROOF . It is clear that we may suppose without loss of generality that λ = 0. By Corollary 24 ( b ) , Corollary XII.4.13 , and ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero