Functional Analysis1969 - Functional analysis - 456 pages |
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A₁ A₂ adjoint algebra algelna analytic Assume B-space Banach space bounded bounded operator called Cauchy closed linear subspace closure commutative compact cont continuous converges convex set Corollary countable Define f(T dense equivalent finite dimensional Gelfand representation H₂ Hahn-Banach Hilbert space homomorphism ideal implies invertible isomorphism K₁ K₂ Kernel Lebesgue Lebesgue measure Lemma Let f LIBRARIES STANFORD UNIVERSITY linear functional linear space linear subspace measure mult multiplication norm open mapping theorem p₁ pointwise polynomial Proof Prop prove R₂ range Riesy S₁ S₂ self-adjoint sequence Simple to check Spectral Theory spectrum STANFORD UNIVERSITY LIBRARIES strong operator topology strongly 1-1 subset Suppose T-XI T+iI T₂ TEL(A TELCA Ts.a UNIVERSITY LIBRARIES STANFORD weak topology weakly x₁ XI-T ZI-T