Linear Operators: Spectral theory |
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Page 1800
... Banach space . Trans . Amer . Math . Soc . 69 , 105-131 ( 1950 ) . Branch points of solutions of equations in Banach ... spaces . Duke Math . J. 8 , 763–770 ( 1941 ) . Reflexive Banach spaces not isomorphic to uniformly convex spaces ...
... Banach space . Trans . Amer . Math . Soc . 69 , 105-131 ( 1950 ) . Branch points of solutions of equations in Banach ... spaces . Duke Math . J. 8 , 763–770 ( 1941 ) . Reflexive Banach spaces not isomorphic to uniformly convex spaces ...
Page 1845
... spaces of continuous functions over a compact space . Amer . J. Math . 71 , 701-705 ( 1949 ) . A theorem of the Hahn - Banach ... spaces and of functions on uniform spaces . Osaka Math . J. 1 , 166–181 ( 1949 ) . Nagumo , M. 1. Einige ...
... spaces of continuous functions over a compact space . Amer . J. Math . 71 , 701-705 ( 1949 ) . A theorem of the Hahn - Banach ... spaces and of functions on uniform spaces . Osaka Math . J. 1 , 166–181 ( 1949 ) . Nagumo , M. 1. Einige ...
Page 1869
... Banach spaces . Revista Ci . , Lima 42 , 355–366 ( 1940 ) ; 43 , 465-474 ( 1941 ) ; 44 , 45-63 ( 1942 ) . 3 . 4 . The weak topologies of Banach spaces . Proc . Nat . Acad . Sci . U.S.A. 25 , 438-440 ( 1939 ) . On certain Banach spaces ...
... Banach spaces . Revista Ci . , Lima 42 , 355–366 ( 1940 ) ; 43 , 465-474 ( 1941 ) ; 44 , 45-63 ( 1942 ) . 3 . 4 . The weak topologies of Banach spaces . Proc . Nat . Acad . Sci . U.S.A. 25 , 438-440 ( 1939 ) . On certain Banach spaces ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero