Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 36
Page 894
... additive operator valued set functions whose values on a set o Є Σ are g ( t ) E ( dt ) , respectively . The integral ss f ( s ) E ( ds E ( od ) , d ) is itself a bounded additive set function for 8 in 2 , and thus the integral of a ...
... additive operator valued set functions whose values on a set o Є Σ are g ( t ) E ( dt ) , respectively . The integral ss f ( s ) E ( ds E ( od ) , d ) is itself a bounded additive set function for 8 in 2 , and thus the integral of a ...
Page 958
... set function y is additive on B 。. There- fore , if eep , the set function μo satisfies the equation μ 。( e1 ~ e2 ) = ( x ( e1 U е2 ) , y ( е1 U е2 ) ) = = ( y ( e1 ) + y ( e2 ) , y ( e1 ) +4 ( e2 ) ) ( y ( e1 ) , y ( e1 ) ) + ( y ...
... set function y is additive on B 。. There- fore , if eep , the set function μo satisfies the equation μ 。( e1 ~ e2 ) = ( x ( e1 U е2 ) , y ( е1 U е2 ) ) = = ( y ( e1 ) + y ( e2 ) , y ( e1 ) +4 ( e2 ) ) ( y ( e1 ) , y ( e1 ) ) + ( y ...
Page 1899
... Additive set function . ( See Set func- tion ) Adjoint element , in an algebra with involution , ( 40 ) . ( See also Ad- joint space ) Adjoint of an operator , between B- spaces , VI.2 compact operator , VI.5.2 ( 485 ) , VI.5.6 ( 486 ) ...
... Additive set function . ( See Set func- tion ) Adjoint element , in an algebra with involution , ( 40 ) . ( See also Ad- joint space ) Adjoint of an operator , between B- spaces , VI.2 compact operator , VI.5.2 ( 485 ) , VI.5.6 ( 486 ) ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 other sections not shown
Common terms and phrases
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 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 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 PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero