## Linear Operators, Part 1 |

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Page 373

44] and for integrals by F.

and was also used by Sz.-Nagy [5]. A similar argument may be applied to obtain

this result in any uniformly convex B-space. This generalizes and abstracts a ...

44] and for integrals by F.

**Riesz**[2; p. 456]. Lemma 4.2 is due to F.**Riesz**[8; p. 36]and was also used by Sz.-Nagy [5]. A similar argument may be applied to obtain

this result in any uniformly convex B-space. This generalizes and abstracts a ...

Page 387

In the case of L, O, 1], Theorem 8.1 was announced independently and

simultaneously in 1907 by Fréchet [4] and F.

by Fréchet [5; III. p. 441]. The theorem for L, 0, 1], 1 < p < 00, was demonstrated

by F.

In the case of L, O, 1], Theorem 8.1 was announced independently and

simultaneously in 1907 by Fréchet [4] and F.

**Riesz**[9]. A detailed proof was givenby Fréchet [5; III. p. 441]. The theorem for L, 0, 1], 1 < p < 00, was demonstrated

by F.

Page 388

1363) and F.

strongly to f in L,(S, X, u) if and only if it converges weakly and f, -> |f|. This

theorem remains valid in any uniformly convex B-space. Theorem 8.15 was

proved ...

1363) and F.

**Riesz**[13]. THEOREM. If I < p < 00 then a sequence {fi} convergesstrongly to f in L,(S, X, u) if and only if it converges weakly and f, -> |f|. This

theorem remains valid in any uniformly convex B-space. Theorem 8.15 was

proved ...

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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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