Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 in Theorem 3 shows that for all n = 1 , 2 , .... ' n 5. Spectral Representation Let μ be a finite positive ... given by the formula ( F ( T ) x ) ( 2 ) F ( 2 ) x ( 2 ) . Our first purpose in this section is to show that , in a ...
... given in Theorem 3 shows that for all n = 1 , 2 , .... ' n 5. Spectral Representation Let μ be a finite positive ... given by the formula ( F ( T ) x ) ( 2 ) F ( 2 ) x ( 2 ) . Our first purpose in this section is to show that , in 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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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 Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero