Linear Operators, Part 2 |
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Page 884
... given here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in greater generality . A simple direct proof of Corollary 3.6 was given by Fukamiya [ 2 ] , and can be used to prove Lemma 3.5 . Corollary 3.10 ...
... given here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in greater generality . A simple direct proof of Corollary 3.6 was given by Fukamiya [ 2 ] , and can be used to prove Lemma 3.5 . Corollary 3.10 ...
Page 909
... given by the formula ( F ( T ) x ) ( 2 ) = F ( λ ) x ( 2 ) . Our first purpose in this section is to show that , in a sense , the example just given is typical of the structure of every normal operator . More explicitly , if T is a ...
... given by the formula ( F ( T ) x ) ( 2 ) = F ( λ ) x ( 2 ) . Our first purpose in this section is to show that , in a sense , the example just given is typical of the structure of every normal operator . More explicitly , if T is a ...
Page 1273
... given by Freudenthal [ 3 ] , of Friedrichs ' proof is the one presented in the text . For another proof of the theorem , see Calkin [ 3 ] and Eberlein [ 2 ; p . 699 ] , and for applications to partial differential equations , consult ...
... given by Freudenthal [ 3 ] , of Friedrichs ' proof is the one presented in the text . For another proof of the theorem , see Calkin [ 3 ] and Eberlein [ 2 ; p . 699 ] , and for applications to partial differential equations , consult ...
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 domain 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 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 subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero