## Functional Analysis: A Short Course |

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addition analysis applied arising assume balanced Banach algebra Banach space bounded called Cauchy Chapter choose closed collection commutative compact complete conclude conjugate consider containing convergence countable defined definition denote distribution domain equivalent establishes example EXERCISE exists extension fact Finally finite follows Given Hausdorff hence Hilbert space ideas identity important induction inequality integral invertible isomorphism Lemma limit linear transformation locally convex space mapping means measure monotone multiplication natural neighborhood neighborhood base nonnegative normal normed linear space Note obtain operator orthogonal orthonormal points positive Problem projection PROOF properties Prove provides quantum mechanics recall respect result Riemann integral satisfying seen self-adjoint seminorm sequence shown subset subspace Theorem theory tion topology unique unit weak yields