Linear Operators, Part 2 |
From inside the book
Results 1-3 of 81
Page 888
... spectral sets and where & is the void set . Here we have used the notations A ^ B and A v B for the intersection and ... operator I in its range . Thus with every bounded operator T in a complex B - space is associated , by means of ...
... spectral sets and where & is the void set . Here we have used the notations A ^ B and A v B for the intersection and ... operator I in its range . Thus with every bounded operator T in a complex B - space is associated , by means of ...
Page 889
... spectral measure which satisfies , instead of ( iii ) , the condition . ( iv ) E ( 8 ) TTE ( 8 ) , a ( Ts ) CỖ , where & is the closure of 8. As will be seen in the next section , a normal operator T in Hilbert space H determines a spectral ...
... spectral measure which satisfies , instead of ( iii ) , the condition . ( iv ) E ( 8 ) TTE ( 8 ) , a ( Ts ) CỖ , where & is the closure of 8. As will be seen in the next section , a normal operator T in Hilbert space H determines a spectral ...
Page 1920
... Spectral asymptotics , XIII.10.G ( 1614 ) Spectral measure , X.1 ( 888 ) countably additive , X.I ( 889 ) self adjoint , X.I ( 892 ) Spectral multiplicity theory , defini- tion , X.5 ( 913 ) Spectral radius , definition , VII.3.5 ( 567 ) ...
... Spectral asymptotics , XIII.10.G ( 1614 ) Spectral measure , X.1 ( 888 ) countably additive , X.I ( 889 ) self adjoint , X.I ( 892 ) Spectral multiplicity theory , defini- tion , X.5 ( 913 ) Spectral radius , definition , VII.3.5 ( 567 ) ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
Other editions - View all
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