Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 λ € and any closed set Д , CA with 20 # 4 , 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 λ € and any closed set Д , CA with 20 # 4 , 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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero