Linear Operators, Part 2 |
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Page 1849
... metric Boolean algebras and vector lattices . J. Sci . Hirosima Univ . Ser . A. 11 , 125-128 ( 1942 ) . On Fréchet lattices , I. J. Sci . Hirosima Univ . Ser . A. 12 , 235-248 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 544 ( 1949 ) ...
... metric Boolean algebras and vector lattices . J. Sci . Hirosima Univ . Ser . A. 11 , 125-128 ( 1942 ) . On Fréchet lattices , I. J. Sci . Hirosima Univ . Ser . A. 12 , 235-248 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 544 ( 1949 ) ...
Page 1913
... metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite ... Metric ( s ) , I.6.1 ( 18 ) invariant , in a linear space , II.1.10 ( 51 ) in a group , ( 90–91 ) topology in normed ...
... metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite ... Metric ( s ) , I.6.1 ( 18 ) invariant , in a linear space , II.1.10 ( 51 ) in a group , ( 90–91 ) topology in normed ...
Page 1921
... metric , definition , I.6.1 ( 18 ) metric or strong , in a B - space , ( 419 ) study of , 1.6 norm or strong , in a normed linear space , II.3.1 ( 59 ) product , definition , I.8.1 ( 32 ) of real numbers , ( 11 ) study of , I.4-8 ...
... metric , definition , I.6.1 ( 18 ) metric or strong , in a B - space , ( 419 ) study of , 1.6 norm or strong , in a normed linear space , II.3.1 ( 59 ) product , definition , I.8.1 ( 32 ) of real numbers , ( 11 ) study of , I.4-8 ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero