Linear Operators, Part 2 |
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Page 855
... Chapter IX is an introduction to the much larger subject of B - algebras ; it serves us as a basis for the spectral theory of bounded self adjoint operators which is presented in Chapter X. Chapters X and XII constitute a relatively ...
... Chapter IX is an introduction to the much larger subject of B - algebras ; it serves us as a basis for the spectral theory of bounded self adjoint operators which is presented in Chapter X. Chapters X and XII constitute a relatively ...
Page 887
... Chapter VII for general opera- tors in a complex B - space . Although the present chapter is independ- ent of Chapter VII , it may help in motivating the study of normal operators if we interpret the reduction problem in the light of ...
... Chapter VII for general opera- tors in a complex B - space . Although the present chapter is independ- ent of Chapter VII , it may help in motivating the study of normal operators if we interpret the reduction problem in the light of ...
Page 1185
Nelson Dunford, Jacob T. Schwartz. CHAPTER XII Unbounded Operators in Hilbert Space 1. Introduction In the preceding chapter we have seen how the spectral theory developed in Chapters IX and X may be applied to various problems in ...
Nelson Dunford, Jacob T. Schwartz. CHAPTER XII Unbounded Operators in Hilbert Space 1. Introduction In the preceding chapter we have seen how the spectral theory developed in Chapters IX and X may be applied to various problems in ...
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