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 = U1I 。= I。· 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 = U1I 。= I。· 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
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