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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction.................................................................................................................................................. 5
Section 1. Notation basic fact and preliminary results....................................................................... 8
Section 2. Some results on Banach lattices......................................................................................... 12
Section 3. Ideals families of sets in a Banach space and Schwartz operator ideals................... 22
Section 4. Schwartz ideals determined by a Banach lattice.............................................................. 26
Section 5. Banach function lattices and the duality theorem of Schwartz..................................... 42
Section 6. Schwartz ideals determined by unconditional basic sequences in $L_p{0, 1)$........ 61
Section 7. Some concluding remarks and some open problems................................................... 68
References.................................................................................................................................................. 61
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
109
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CIX
Daty
wydano
1973
Twórcy
autor
- Institute of Mathematics, Arhus University, Århus, Denmark
Bibliografia
- [1] D. Amir and. J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), pp. 35-46.
- [2] W. Bade, The Banach space C(S), Lecture Note Series 26, Aarhus University 1969-1970.
- [3] A. Badrikian, Séminaire sur les fonctions aléatoires linéaires et les measures cylindriques, Université de Clermont 1969.
- [4] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), pp. 151-164.
- [5] H. F. Bohnenblust, An axiomatic characterization of $L_p$-spaces, Duke Math. J. 6 (1940), pp. 627-640.
- [6] M. M. Day, Normed linear spaces, Berlin-Göttingen-Heidelberg 1958.
- [7] E. Dubinski and M. S. Ramanujan, On Λ-nuclearity, to appear.
- [8] E. Dubinski, A. Pełczyński and H. P. Rosenthal, On Banach spaces X, for which, $П_2[ℒ_∞, X) = B{ℒ_∞, X)$, Studia Math. 44 (1973) pp. 617-648.
- [9] N. Dunford and J. T. Schwartz, Linear operators, part 1, London, New York 1958.
- [10] V. F. Gaposhkin, On a property of unconditional basis in $L_p$, Uspehi Matem. Nauk 14, 4 (88) (1959), pp. 143-148 (Russian).
- [11] A. Grothendieck, Produits tensoriels et espaces nucléaire, Mem. Amer. Math. Soc. 16 (1955).
- [12] A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. V (1953), pp. 129-173.
- [13] W. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math. 9, no. 4 (1971), pp. 488-506.
- [14] J. Hoffmann Jørgensen, The theory of analytic spaces, Various Publication Series 10, Aarhus University 1970.
- [15] M. I. Kadec and A. Pełczyński, Bases, lacunary sequences and complemented subspaces $L_p$, Studia Math. 21 (1962), pp. 161-176.
- [16] S. Kakutani, Concrete representations of abstract M-spaces, Ann. of Math. 42, no. 4 (1941), pp. 994-1024.
- [17] S. Kwapień, On a theorem of L. Schwartz, Studia Math. 38 (1970), pp. 193-201.
- [18] J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in $L_p$-spaces and their applications, Studia Math. 29 (1968), pp. 276-326.
- [19] J. Lindenstrauss and H. P. Rosenthal, The $L_p$-spaces, Israel J. Math. 7 (1969), pp. 325-349.
- [20] W. A. J. Luxemburg, Banach Function Spaces, Van Gorcum-Assen. 1965.
- [21] A. Pełczyński, Projection in certain Banach spaces, Studia Math. 19 (1960), pp. 209-228.
- [22] A. J. Peressini, Ordered topological vector spaces, New York 1967.
- [23] A. Persson, On some properties of p-nuclear and p-integral operators, Studia Math. 33 (1969), pp. 213-222.
- [24] A. Persson and A. Pietsch, p-nukleäre und p-integrale Abbildungen in Banachraümen, Studia Math. 33 (1969), pp. 19-61.
- [25] A. Pietsch, Absolut p-summierende Abbildungen in normierten Räumen, Studia Math. 28 (1967), pp. 333-353.
- [26] M. M. Rao, Linear operations, tensor products, and contractive projections in function spaces, Studia Math. 38 (1970), pp. 131-186.
- [27] H. P. Rosenthal, On injective Banach spaces and the spaces $L_∞(μ)$ for finite measures μ, Acta Math. 124 (1970), pp. 205-247.
- [28] H. P. Rosenthal, On subspaces of $L_p$, Ann. of Math. 97 (1973), pp. 344-373.
- [29] H. H. Schaefer, Topological vector spaces, 1966.
- [30] L. Schwartz, Applications p-radonifiantes et le théorème de dualité, Studia Math. 38 (1970), pp. 203-213.
- [31] Applications radonifiantes, Seminaire Paris 1969-1970.
- [32] Z. Semadeni, Banach spaces of continuous functions, Warszawa 1971.
- [33] S. Simmons, Local reflexivity and (p, q)-summing maps, to appear.
- [34] C. and A. Ionescu-Tulcca, On the lifting property, J. Math. Anal, and Appl. 3 (1961), pp. 537-546.
- [35] L. Tzafriri, A isomorphic characterization of $L_p$ and $c_0$-spaces, Michigan Math. J. 18, no. 1, (1971), pp. 21-31.
- [36] L. Tzafriri, Reflexivity in Banach lattices and their subspaces, J. Funct. Analysis, 10, no. 1 (1972), pp. 1-18.
- [37] M. Zippin, On perfectly homogeneous bases in Banach spaces, Israel J. Math. 4 (1966), pp. 265-272.
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