## Linear Operators: General theory |

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Page 67

23 Theorem. A closed linear manifold in a

Let ?J be a closed linear manifold in the

defined by the equation f (x*)y = x*y, y cty. Clearly \£{x*)\ ^ |**|, so that f : X* -»□?)

*.

23 Theorem. A closed linear manifold in a

**reflexive**B-space is**reflexive**. Proof.Let ?J be a closed linear manifold in the

**reflexive**space X. Let £ : x* -*y* bedefined by the equation f (x*)y = x*y, y cty. Clearly \£{x*)\ ^ |**|, so that f : X* -»□?)

*.

Page 88

conjugate is isometric was proved by Hahn [3; p. 219] who was the first to

formulate the notion of the conjugate space. He used the term regular to describe

what ...

**Reflexivity**. The fact that the natural isomorphism of a fi-space 3E into its secondconjugate is isometric was proved by Hahn [3; p. 219] who was the first to

formulate the notion of the conjugate space. He used the term regular to describe

what ...

Page 425

Proof. The X*-closure of x(X) is a subspace of X**, which, by Theorem 5, contains

the unit sphere of 36**. It follows immediately that it contains every point in X**.

Q.E.D. Theorems 2 and 5 lead to an important result on

Proof. The X*-closure of x(X) is a subspace of X**, which, by Theorem 5, contains

the unit sphere of 36**. It follows immediately that it contains every point in X**.

Q.E.D. Theorems 2 and 5 lead to an important result on

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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