## Linear Operators: General theory |

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Page 240

The space bs is the linear space of all sequences x — {x„} of

norm n \x\ = sup | ]T(x>| n <=1 is finite. 11. ... tcS A

measurable if f~1(A)eE for every Borel set A in the range of /. It is clear that every

...

The space bs is the linear space of all sequences x — {x„} of

**scalars**for which thenorm n \x\ = sup | ]T(x>| n <=1 is finite. 11. ... tcS A

**scalar**function / on S is E-measurable if f~1(A)eE for every Borel set A in the range of /. It is clear that every

...

Page 256

If, however, each of the spaces 3£j X„ are Hilbert spaces then it will always be

understood, sometimes without explicit mention, that X is the uniquely

determined Hilbert space with

•, •)< is the ...

If, however, each of the spaces 3£j X„ are Hilbert spaces then it will always be

understood, sometimes without explicit mention, that X is the uniquely

determined Hilbert space with

**scalar**product n (iv) (fo «»], y„]) = 2 yi)i, «=i where (•, •)< is the ...

Page 323

A

sequence {/„} of simple functions such that (i) fn(s) converges to f(s) //-almost

everywhere; (ii) the sequence {J£/b(*)/m(^)} converges in the norm of X for each

Eel.

A

**scalar**valued measurable function / is said to be integrable if there exists asequence {/„} of simple functions such that (i) fn(s) converges to f(s) //-almost

everywhere; (ii) the sequence {J£/b(*)/m(^)} converges in the norm of X for each

Eel.

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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