## Linear Operators, Part 1 |

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Page 37

If T; 3 - ?) and U : ) → 3 are linear transformations, and 3, 9), 3 are linear spaces

over the same field q}, the product UT, defined by (UT)r = U(Tw), is a linear

transformation which maps 3 into 3. If T is a

be a ...

If T; 3 - ?) and U : ) → 3 are linear transformations, and 3, 9), 3 are linear spaces

over the same field q}, the product UT, defined by (UT)r = U(Tw), is a linear

transformation which maps 3 into 3. If T is a

**linear operator**on 3 to 3, it is said tobe a ...

Page 486

Linear combinations of compact

product of a compact

Linear combinations of compact

**linear operators**are compact operators, and anyproduct of a compact

**linear operator**and a bounded**linear operator**is a compact**linear operator**. PRoof. The conclusions of Theorem 4 follow readily from the ...Page 513

13 If U : )* → ** is a linear mapping which is continuous with the Q) topology in Q

)* and the 3' topology in 3", then there exists a bounded

such that To = U. 14 Let T be a linear, but not necessarily continuous, mapping ...

13 If U : )* → ** is a linear mapping which is continuous with the Q) topology in Q

)* and the 3' topology in 3", then there exists a bounded

**linear operator**T : * –- ?)such that To = U. 14 Let T be a linear, but not necessarily continuous, mapping ...

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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

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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