Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 31
Page 875
... homomorphism of a B * -algebra X into a B * -algebra is a homomorphic map h of X into which preserves involutions , i.e. , h ( x ) * = h ( x * ) . A * -isomorphism between the B * - algebras X and Y is a * -homomorphism h of X into Y ...
... homomorphism of a B * -algebra X into a B * -algebra is a homomorphic map h of X into which preserves involutions , i.e. , h ( x ) * = h ( x * ) . A * -isomorphism between the B * - algebras X and Y is a * -homomorphism h of X into Y ...
Page 980
... homomorphisms are continuous ( Corollary IX.2.3 ) . Since every non - zero complex valued homomorphism H on either A or A1 is continuous and has H ( I ) = 1 it follows that H is completely determined by the values it takes on elements ...
... homomorphisms are continuous ( Corollary IX.2.3 ) . Since every non - zero complex valued homomorphism H on either A or A1 is continuous and has H ( I ) = 1 it follows that H is completely determined by the values it takes on elements ...
Page 981
... homomorphism on A1 . Thus the map H → H1 defines a map of M into M1 . Since these homomorphisms are continuous ( IX.2.3 ) and 2 , is dense in A this map is one - to - one . To see that the range of this map is all of M1 let H1 be any ...
... homomorphism on A1 . Thus the map H → H1 defines a map of M into M1 . Since these homomorphisms are continuous ( IX.2.3 ) and 2 , is dense in A this map is one - to - one . To see that the range of this map is all of M1 let H1 be any ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
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