Linear Operators: Spectral theory |
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Page 900
... bounded 2 - measurable function , i.e. , an element of the B * -algebra B ... operators in Hilbert space is a continuous * -homomorphism . The next result shows ... operator if and only if 1 / f is E - essentially bounded on S ; ( iii ) o ...
... bounded 2 - measurable function , i.e. , an element of the B * -algebra B ... operators in Hilbert space is a continuous * -homomorphism . The next result shows ... operator if and only if 1 / f is E - essentially bounded on S ; ( iii ) o ...
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 ( 2 ; 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 ( 2 ; 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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero