## Linear Operators, Part 1 |

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Page 240

The space bs is the linear space of all sequences w = {2,} of

norm |a = sup Sz. n i-1 is finite. 11. The space cs is the linear space of all

sequences a = {x,} for which the series X. A 2, is convergent. The norm is |a = sup

|X 2, .

The space bs is the linear space of all sequences w = {2,} of

**scalars**for which thenorm |a = sup Sz. n i-1 is finite. 11. The space cs is the linear space of all

sequences a = {x,} for which the series X. A 2, is convergent. The norm is |a = sup

|X 2, .

Page 256

If, however, each of the spaces 3:1, ..., *, are Hilbert spaces then it will always be

understood, sometimes without explicit mention, that 3 is the uniquely determined

Hilbert space with

If, however, each of the spaces 3:1, ..., *, are Hilbert spaces then it will always be

understood, sometimes without explicit mention, that 3 is the uniquely determined

Hilbert space with

**scalar**product (iv) (a1, • * * * an], st/1. • * > !/...]) -2. (a', U.) ...Page 323

A

sequence {f,} of simple functions such that (i) fo(s) converges to f(s) u-almost

everywhere; (ii) the sequence {sef,(s)u(ds)} converges in the norm of 3 for each

Ee 2.

A

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

everywhere; (ii) the sequence {sef,(s)u(ds)} converges in the norm of 3 for each

Ee 2.

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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