## Topics in analysis: (Mathematics 609) |

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### Contents

Chapter 1 | 2-1 |

Chapter 4 | 2-4 |

N I Akhieser and I M Glazman Theory of linear operators in Hilbert | 3-1 |

8 other sections not shown

### Common terms and phrases

adjoint aeF aeF Banach space bounded linear C*-algebra Cauchy closed subalgebra closed subspace commutative Banach algebra containing continuous function converges Corollary Define Definition Let dim ker eigenvalue extremely disconnected f e C(X f e H f e ker f,g e finite dimensional finite rank operator Fredholm Gelfand map Gelfand transform given Hausdorff space Hence Hilbert space homeomorphism idempotent Inequality inner product invertible in H isometric isomorphism ker Q Lemma Let f e lim sup linear space llfll2 maximal ideal space multiplicative linear functional norm one-to-one open and closed open mapping open mapping theorem orthonormal pointwise polar decomposition polynomials Proof Let Proof Suppose Proposition Let prove range Re(Tf,g self-adjoint separates points sequence subset Suppose f Tf,g two-sided ideal unilateral shift unique vector weak topology