Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1188
... defined by the identity ( Tx , y ) = ( x , T * y ) . We shall need to use the notion of the Hilbert space adjoint of an operator which is not necessarily bounded and this concept is formulated in the following definition . 4 DEFINITION ...
... defined by the identity ( Tx , y ) = ( x , T * y ) . We shall need to use the notion of the Hilbert space adjoint of an operator which is not necessarily bounded and this concept is formulated in the following definition . 4 DEFINITION ...
Page 1196
... defined in Definition 1.1 or as in Definition VII.9.6 . This is the case , as will be shown in Corollary 8 below , so that the symbol f ( T ) for a polynomial fis unambiguously defined . 6 THEOREM . Let E be the resolution of the ...
... defined in Definition 1.1 or as in Definition VII.9.6 . This is the case , as will be shown in Corollary 8 below , so that the symbol f ( T ) for a polynomial fis unambiguously defined . 6 THEOREM . Let E be the resolution of the ...
Page 1548
... defined for the self adjoint operators T and Î as in Exercise D2 . Show that λ ( T ) ≥ ¿ „ ( Î ) , n ≥ 1 . 1 D11 Let T1 be a self adjoint operator in Hilbert space H1 , and let T2 be a self adjoint operator in Hilbert space 2. Define ...
... defined for the self adjoint operators T and Î as in Exercise D2 . Show that λ ( T ) ≥ ¿ „ ( Î ) , n ≥ 1 . 1 D11 Let T1 be a self adjoint operator in Hilbert space H1 , and let T2 be a self adjoint operator in Hilbert space 2. Define ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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