## Linear Operators, Part 1 |

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Page 251

It is clear that E is a projection, i.e., E* = E, and that E is an

It is the uniquely determined

It is clear that E is a projection, i.e., E* = E, and that E is an

**orthogonal**projection.It is the uniquely determined

**orthogonal**projection with EX) = }]'. For if D is an**orthogonal**projection with DX) = \st then ED = D and, since (I–D)\) C S) e Jú, we ...Page 357

Exercises on

exercises is concerned with the application of linear space methods to the theory

of

Fourier ...

Exercises on

**Orthogonal**Series and Analytic Functions The following set ofexercises is concerned with the application of linear space methods to the theory

of

**orthogonal**series. The most important special case of this theory is that ofFourier ...

Page 851

... definition, IV.4.3 (249) properties, IV.4.4 (249), IV.4.18 (256)

complement of a set in a normed space, II.4.17 (72) remarks on, (93)

elements and manifolds in Hilbert space, IV.4.3 (249)

Hilbert ...

... definition, IV.4.3 (249) properties, IV.4.4 (249), IV.4.18 (256)

**Orthogonal**complement of a set in a normed space, II.4.17 (72) remarks on, (93)

**Orthogonal**elements and manifolds in Hilbert space, IV.4.3 (249)

**Orthogonal**projections inHilbert ...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero