Linear Operators: Spectral theory |
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Page 900
... bounded -measurable function , i.e. , an element of the B * -algebra B ( S ... operators in f Hilbert space is a continuous * -homomorphism . The next result ... operator if and only if 1 / f is E - essentially bounded on S ; ( iii ) a ...
... bounded -measurable function , i.e. , an element of the B * -algebra B ( S ... operators in f Hilbert space is a continuous * -homomorphism . The next result ... operator if and only if 1 / f is E - essentially bounded on S ; ( iii ) a ...
Page 1187
... bounded operator the resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( λ ; T ) will be used ...
... bounded operator the resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( λ ; T ) will be used ...
Page 1273
... operator with at least one real number in y ( T ) , then the deficiency indices are equal . This latter result was established by Calkin [ 3 ] . ) Semi - bounded operators . Von Neumann [ 7 ; p . 103 ] proved that a semi - bounded ...
... operator with at least one real number in y ( T ) , then the deficiency indices are equal . This latter result was established by Calkin [ 3 ] . ) Semi - bounded operators . Von Neumann [ 7 ; p . 103 ] proved that a semi - bounded ...
Contents
BAlgebras | 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 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