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Page 868
... a commutative B - algebra every ideal is two - sided and the quotient algebra X / 3 is again a commutative algebra ... field of complex numbers if and only if I is maximal . PROOF . If is not maximal it is properly contained in an ideal and ...
... a commutative B - algebra every ideal is two - sided and the quotient algebra X / 3 is again a commutative algebra ... field of complex numbers if and only if I is maximal . PROOF . If is not maximal it is properly contained in an ideal and ...
Page 932
... of contractions are found in Sz . - Nagy [ 8 , 10 ] ( see also Cooper [ 3 ] ) . Sz . - Nagy's original proof depended on the following theorem due to Neumark [ 3 ] . THEOREM . Let S be an abstract set and Σ a field ( resp . o - field ) of ...
... of contractions are found in Sz . - Nagy [ 8 , 10 ] ( see also Cooper [ 3 ] ) . Sz . - Nagy's original proof depended on the following theorem due to Neumark [ 3 ] . THEOREM . Let S be an abstract set and Σ a field ( resp . o - field ) of ...
Page 1641
... a not in U , and that g takes on only non - negative values . Let & be the ... field of sets . If { f } is an increasing sequence of characteristic ... the conclusion of the first paragraph of XIV.2.2 NOTATIONAL CONVENTIONS AND PRELIMINARIES ...
... a not in U , and that g takes on only non - negative values . Let & be the ... field of sets . If { f } is an increasing sequence of characteristic ... the conclusion of the first paragraph of XIV.2.2 NOTATIONAL CONVENTIONS AND PRELIMINARIES ...
Contents
BAlgebras | 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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero