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Linear Algebra and Analysis
Linear Mappings and Operators
7 other sections not shown
adjoint Banach space Cauchy sequence choose Clearly closed set commutes compact operator compact set complex number continuous function Corollary countable defined Definition 1 Let denote dense in H diagonalizable discussion eigenspace eigenvalue eigenvector equation Exercises 4.2 finite dimensional fixed follows G D(T given Hamel basis hence Hilbert space implies infinite inner product space integral invertible isometrically isomorphic Lemma Let us show linear manifold linear map linear operator linear subspace linearly independent matrix non-zero normal operator normed space null space one-to-one operator on H orthogonal projection orthonormal basis orthonormal set pn(t polynomial problem projection of H Proof prove real numbers real-valued recall scalars Section 2.4 self-adjoint operator space and let space H spectral theorem spectrum subset subspace of H Suppose unit ball unitary operator vector space weakly convergent zero vector