Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 28
Page 912
... separable then the measure space ( S , E , μ ) in Corollary 4 may be taken to be finite . PROOF . If is separable then there are a countable number of mutually orthogonal admissible spaces $ ,, n = 1 , 2 , . . . , which span n n 12 - 1 ...
... separable then the measure space ( S , E , μ ) in Corollary 4 may be taken to be finite . PROOF . If is separable then there are a countable number of mutually orthogonal admissible spaces $ ,, n = 1 , 2 , . . . , which span n n 12 - 1 ...
Page 928
... separable Hilbert space , and let T be a bounded operator which commutes with every operator which commutes with A. Then there exists a bounded measurable function f such that T = f ( A ) . This theorem was stated explicitly by F. Riesz ...
... separable Hilbert space , and let T be a bounded operator which commutes with every operator which commutes with A. Then there exists a bounded measurable function f such that T = f ( A ) . This theorem was stated explicitly by F. Riesz ...
Page 1918
... Separability and metrizability , V.5.1-2 ( 426 ) Separable linear manifolds , II.1.5 ( 50 ) . ( See also Separable sets ) in C , IV.13.16 ( 340 ) in L ,, III.8.5 ( 168 ) , III.9.6 ( 169 ) Separable sets , 1.6.11 ( 21 ) . ( See also ...
... Separability and metrizability , V.5.1-2 ( 426 ) Separable linear manifolds , II.1.5 ( 50 ) . ( See also Separable sets ) in C , IV.13.16 ( 340 ) in L ,, III.8.5 ( 168 ) , III.9.6 ( 169 ) Separable sets , 1.6.11 ( 21 ) . ( See also ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 other sections not shown
Other editions - View all
Common terms and phrases
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