Linear Operators, Part 2 |
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Page 900
... bounded E - 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 E - 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 | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero