## Linear Operators: General theory |

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Page 243

The norm in § is \x\ = (a;, a;)1/a. Remark.

of abstract axioms. It is noteworthy that some of the concrete spaces defined

above satisfy these axioms, and hence are special cases of abstract

The norm in § is \x\ = (a;, a;)1/a. Remark.

**Hilbert space**has been defined by a setof abstract axioms. It is noteworthy that some of the concrete spaces defined

above satisfy these axioms, and hence are special cases of abstract

**Hilbert****space**.Page 247

closely related, especially in its elementary geometrical aspects, to the Euclidean

or finite dimensional unitary spaces. It is not immediate from the definition (2.26) ...

**Hilbert Space**Of the infinite dimensional B-spaces,**Hilbert space**is the mostclosely related, especially in its elementary geometrical aspects, to the Euclidean

or finite dimensional unitary spaces. It is not immediate from the definition (2.26) ...

Page 256

Whenever the direct sum of normed linear spaces is used as a normed space,

the norm will be explicitly mentioned. If, however, each of the spaces 3£j X„ are

mention ...

Whenever the direct sum of normed linear spaces is used as a normed space,

the norm will be explicitly mentioned. If, however, each of the spaces 3£j X„ are

**Hilbert spaces**then it will always be understood, sometimes without explicitmention ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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