Linear Operators, Part 2 |
From inside the book
Results 1-3 of 49
Page 872
... topological space . 0 = 15 DEFINITION . A topological space A is completely regular if sets consisting of single points are closed and if for any point 20 € A and any closed set 4 CA with 20 # 4o there is a continuous function f defined ...
... topological space . 0 = 15 DEFINITION . A topological space A is completely regular if sets consisting of single points are closed and if for any point 20 € A and any closed set 4 CA with 20 # 4o there is a continuous function f defined ...
Page 1150
... topological space , a fact that was occasionally used in the text . Next we shall state the fundamental theorem concerning the existence of Haar measure and prove some of the more important elementary properties of this measure which ...
... topological space , a fact that was occasionally used in the text . Next we shall state the fundamental theorem concerning the existence of Haar measure and prove some of the more important elementary properties of this measure which ...
Page 1921
... space , definition , VII.7 ( 458 ) Strictly convex B - space , definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11– 12 ( 512-513 ) Strong topology , in a normed space ...
... space , definition , VII.7 ( 458 ) Strictly convex B - space , definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11– 12 ( 512-513 ) Strong topology , in a normed space ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm 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 transform unique unitary vanishes vector zero