Dissertationes mathematicae; 474 (Warszawa, 2010). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаDissertationes mathematicae. 474: Approximate amenability of semigroup algebras and Segal algebras / H.G.Dales, R.J.Loy; Institute of Mathematics. Polish Academy of Sciences. - Warszawa: Instytut matematyczny PAN, 2010. - 58 p. - Ref.: p.55-58. - ISSN 0012-3862
 

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Оглавление / Contents
 
1  Preliminaries ................................................ 5
   1.1  Background .............................................. 5
   1.2  Amenability for Banach algebras ......................... 7
   1.3  Basic definitions ....................................... 9
   1.4  Intrinsic characterizations ............................ 10
   1.5  Pointwise variations ................................... 12
   1.6  Results concerning ideals .............................. 14
   1.7  Banach function algebras ............................... 16
   1.8  Banach sequence algebras ............................... 17
   1.9  On approximate identities .............................. 25
   1.10 Summary of interrelations .............................. 26
2  Semigroup algebras .......................................... 27
   2.1  Background ............................................. 27
   2.2  The case where E(S) finite ............................. 28
3  A weighted semigroup algebra ................................ 30
   3.1  Basic definitions ...................................... 31
   3.2  The Gel'fand transform ................................. 32
   3.3  An approximate identity ................................ 34
   3.4  Weak amenability and amenability ....................... 34
   3.5  Pointwise amenability .................................. 35
   3.6  Bounded approximate contractibility .................... 36
   3.7  Pointwise approximate amenability ...................... 38
   3.8  Convergence of 'tails' ................................. 39
   3.9  Approximate amenability ................................ 40
   3.10 Summary ................................................ 42
   3.11 A subsidiary example ................................... 43
4  Segal algebras .............................................. 44
   4.1  Introduction ........................................... 44
   4.2  The approximate amenability of Segal algebras on fig.3 .... 46
   4.3  Segal algebras on fig.2 ................................... 50
   4.4  The pointwise approximate amenability of Segal 
        algebras on fig.3 ......................................... 54
   4.5  Postscript ............................................. 55
5  Open questions .............................................. 55

References ..................................................... 55


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