Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 83
Page 884
... given here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in greater generality . A simple direct proof of Corollary 3.6 was given by Fukamiya [ 2 ] , and can be used to prove Lemma 3.5 . Corollary 3.10 ...
... given here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in greater generality . A simple direct proof of Corollary 3.6 was given by Fukamiya [ 2 ] , and can be used to prove Lemma 3.5 . Corollary 3.10 ...
Page 909
... given by the formula ( F ( T ) x ) ( 2 ) F ( 2 ) x ( 2 ) . Our first purpose in this section is to show that , in a sense , the example just given is typical of the structure of every normal operator . More explicitly , if T is a normal ...
... given by the formula ( F ( T ) x ) ( 2 ) F ( 2 ) x ( 2 ) . Our first purpose in this section is to show that , in a sense , the example just given is typical of the structure of every normal operator . More explicitly , if T is a normal ...
Page 1149
... given in Weyl's memoir Theorie der Darstellungen kontinuierlicher halb - einfachen Gruppen durch lineare Transformationen III , Math . Zeitschift v . 24 ( 1926 ) p . 377-395 . The representation theory for groups which are neither ...
... given in Weyl's memoir Theorie der Darstellungen kontinuierlicher halb - einfachen Gruppen durch lineare Transformationen III , Math . Zeitschift v . 24 ( 1926 ) p . 377-395 . The representation theory for groups which are neither ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 other sections not shown
Other editions - View all
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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero