Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 875
... shown that the homomorphism x → x ( · ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 4 ) of all continuous functions on the structure space Д of X is an iso- metric isomorphism of X onto all of C ( A ) . It ...
... shown that the homomorphism x → x ( · ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 4 ) of all continuous functions on the structure space Д of X is an iso- metric isomorphism of X onto all of C ( A ) . It ...
Page 981
... shown in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H1 ( T ( ƒ ) ) = √2 h ( x ) f ( x ) dx , 1 1 fe L1 ( R ) . The converse part of Theorem 3.11 shows that such a character determines a ...
... shown in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H1 ( T ( ƒ ) ) = √2 h ( x ) f ( x ) dx , 1 1 fe L1 ( R ) . The converse part of Theorem 3.11 shows that such a character determines a ...
Page 1161
... shown by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been shown by M. Paul Malliavin that spectral synthesis is not possible for all functions on the real axis . Cf. P. Malliavin , Sur l'impossibilité de ...
... shown by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been shown by M. Paul Malliavin that spectral synthesis is not possible for all functions on the real axis . Cf. P. Malliavin , Sur l'impossibilité de ...
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