Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 79
Page 906
... positive definite if it is positive and ( Tx , x ) > 0 for every x 0 in H. = = = = It is clear that all of these classes of operators are normal . Unitary operators have a number of other characteristic proper- ties . For example , if U ...
... positive definite if it is positive and ( Tx , x ) > 0 for every x 0 in H. = = = = It is clear that all of these classes of operators are normal . Unitary operators have a number of other characteristic proper- ties . For example , if U ...
Page 1247
... positive self adjoint transformations and their square roots . = 2 LEMMA . A self adjoint transformation T is positive if and only if o ( T ) is a subset of the interval [ 0 , ∞ ) . PROOF . Let E be the resolution of the identity for T ...
... positive self adjoint transformations and their square roots . = 2 LEMMA . A self adjoint transformation T is positive if and only if o ( T ) is a subset of the interval [ 0 , ∞ ) . PROOF . Let E be the resolution of the identity for T ...
Page 1338
... positive matrix measure whose elements μ are continuous with respect to a positive o - finite measure u . If the matrix of densities { m } is defined by the equations μ ,, ( e ) = f ̧m ,, ( 2 ) μ ( d2 ) , where e is any bounded Borel ...
... positive matrix measure whose elements μ are continuous with respect to a positive o - finite measure u . If the matrix of densities { m } is defined by the equations μ ,, ( e ) = f ̧m ,, ( 2 ) μ ( d2 ) , where e is any bounded Borel ...
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