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$ℒ_p$-Spaces and injective locally convex spaces

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Rozprawy Matematyczne tom/nr w serii: 298 wydano: 1990
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CONTENTS
Introduction.................................................................................................................................................................5
Conventions and notations.........................................................................................................................................8
1. Preliminaries from the theory of locally convex spaces.........................................................................................11
2. Ultraproducts of locally convex spaces.................................................................................................................16
3. The principle of local reflexivity for locally convex spaces.....................................................................................19
4. Complemented subspaces of products and direct sums of Banach $L_p$-spaces and L₁ -predual spaces........24
5. Definition, examples and basic properties of locally convex $ℒ_p$-spaces..........................................................29
6. Definition, examples and basic properties of $Dℒ_p$-spaces..............................................................................39
7. Local properties of complemented subspaces of products and direct sums of Banach $L_p$-spaces................42
8. Duality between $ℒ_p$ and $Dℒ_p$-spaces and a characterization of injective spaces.....................................46
9. Extension, lifting and factorization properties of $ℒ_p$ and $Dℒ_p$-spaces.......................................................56
10. Fréchet $ℒ_p$- and (DF)-&Dℒ_p$-spaces with applications to Fréchet injective spaces..................................62
11. Comments and open problems...........................................................................................................................71
References...............................................................................................................................................................73
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 298
Liczba stron
76
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXCVIII
Daty
wydano
1990
Twórcy
  • Instytut Matematyki, Uniwersytet im. A. Mickiewicza, Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
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Języki publikacji
EN
Uwagi
1985 Mathematics Subject Classification:
Primary 46A05, 46A06, 46A12, 46A20, 46A22, 46A99, 46M10, 03C20;
Secondary 46E10, 46E15, 46E30, 46C99.
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bwmeta1.element.zamlynska-40d0ba71-1eee-43ad-a56e-664a2d136056
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83-01-09882-1
ISSN
0012-3862
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DML-PL
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