Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1120
... assume for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces . Thus , the key to the situation . that we wish to analyze is the ...
... assume for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces . Thus , the key to the situation . that we wish to analyze is the ...
Page 1594
... assume ( a ) the function g is non - negative and piecewise continuous in the interval [ 0 , ∞ ) , ( b ) the ... assume that lim Q ( t ) = ∞ . t → b ( 8 ) ( 7.67 ) In the interval [ a , b ) , let Q be defined as in ( 7 ) , and assume ...
... assume ( a ) the function g is non - negative and piecewise continuous in the interval [ 0 , ∞ ) , ( b ) the ... assume that lim Q ( t ) = ∞ . t → b ( 8 ) ( 7.67 ) In the interval [ a , b ) , let Q be defined as in ( 7 ) , and assume ...
Page 1734
... assume without loss of generality that U1 U1lo = Io . This will be assumed in what follows . Making use of the properties ( i ) and ( ii ) of the mapping 9 , and of Lemmas 3.47 and 3.48 , we see that we may assume without loss of ...
... assume without loss of generality that U1 U1lo = Io . This will be assumed in what follows . Making use of the properties ( i ) and ( ii ) of the mapping 9 , and of Lemmas 3.47 and 3.48 , we see that we may assume without loss of ...
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 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 Haar measure 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 operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF 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