## Linear Operators: General theory |

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Page 733

On bases in Hilbert space. Doklady Akad. Nauk SSSR (X.S.) 69, 483-485 (1949).

(Russian) Math. Rev. 11, 525 (1950). ... Math. Soc. 01, 122-127 (1947). 4.

Spectral resolution of groups of unitary operators.

1944).

On bases in Hilbert space. Doklady Akad. Nauk SSSR (X.S.) 69, 483-485 (1949).

(Russian) Math. Rev. 11, 525 (1950). ... Math. Soc. 01, 122-127 (1947). 4.

Spectral resolution of groups of unitary operators.

**Duke Math**. J. 11 , 589-595 (1944).

Page 773

Math. Soc. 72, 323-326 (1952). !{. The Tychonoff product theorem implies the

axiom of choice. Fund. .Math. 87, 75-76 (1950). 4. Convergence in topology.

York, ...

Math. Soc. 72, 323-326 (1952). !{. The Tychonoff product theorem implies the

axiom of choice. Fund. .Math. 87, 75-76 (1950). 4. Convergence in topology.

**Duke Math**. J. 17, 277-283 (1950). 5. General topology. D. van Nostrand, NewYork, ...

Page 797

Amer. Math. Soc. Colloquium Pub. no. 19, New York, 1934. Paley, R. E. A. C,

Wiener, N\, and Zygmund, A. 1. Notes on random functions. Math. Zeit. 87, 647-

668 (1933). Parker, W. V. 1. Limits to the characteristic roots of a matrix.

Amer. Math. Soc. Colloquium Pub. no. 19, New York, 1934. Paley, R. E. A. C,

Wiener, N\, and Zygmund, A. 1. Notes on random functions. Math. Zeit. 87, 647-

668 (1933). Parker, W. V. 1. Limits to the characteristic roots of a matrix.

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact