References

  1. Albiac F., Kalton N. Topics in Banach Space Theory. Graduate Texts in Math., 233, Springer, New York, 2006.
  2. Alspach D., Enflo P., Odell E. On the structure of separable ${\mathcal L}_p$ spaces (1<p<∞). Stud. Math. 1977, 60, 79-90.
  3. Alspach D., Odell E. $L_p$ spaces. Handbook of the geometry of Banach spaces. Vol. I. Edited by W.B. Johnson and J. Lindenstrauss. North-Holland Publishing Co., Amsterdam, 2001., 123-159.
  4. Banach S.S. Cours of Functional Analysis. Rad. Shkola, Kyiv, 1948 (in Ukrainian). Translation from the book ``Théorie des opérations linéaires'', 1932.
  5. Bennet B., Dor L.E., Goodman V., Johnson W.B., Newman C. M. On uncomplemented subspaces of $L_p$, 1<p<2. Israel J. Math. 1977, 26 (2), 178-187.
  6. Bourgain J. A counterexample to a complementation problem. Compos. Math. 1981, 43 (1), 133-144.
  7. Bourgain J. A characterization of non-Dunford-Pettis operators on $L^1$. Israel J. Math. 1980, 37 (1-2), 48-53.
  8. Bourgain J., Rosenthal H.P., Schechtman G. An ordinal $L^p$-index for Banach spaces, with applications to complemented subspaces of $L^p$. Ann. of Math. (2) 1981, 114 (2), 193-228.
  9. Bretagnolle J., Dacunha-Castelle D., Krivine J.L. Lois stables et espaces $L_p$. Ann. Inst. Henri Poincare, Sér. B. 1966, 2, 231-259.
  10. Burkholder D.L. A nonlinear partial differential equation and the unconditional constant of the Haar system in $L^p$. Bull. Amer. Math. Soc. (N.S.) 1982, 7 (3), 591-595.
  11. Burkholder D.L. An elementary proof of an inequality of R. E. A. C. Paley. Bull. Lond. Math. Soc. 1985, 17 (5), 474-478.
  12. Diestel J., Uhl J.J. Vector Measures. AMS, Mathematical surveys, 1977.
  13. Enflo P., Rosenthal H.P. Some results concerning $L^p(\mu)$-spaces. J. Funct. Anal. 1973, 14 (4), 325-348.
  14. Enflo P., Starbird T. Subspaces of $L^1$ containing $L^1$. Studia Math. 1979, 65 (2), 203-225.
  15. Fremlin D.H., Measure Theory. Vol. 3. Measure algebras. Torres Fremlin, Colchester, 2004.
  16. Grothendieck A. Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. 1955, 16.
  17. Hagler J. A counterexample to several questions about Banach spaces. Studia Math. 1977, 60, 289-308.
  18. Johnson W.B., Maurey B., Schechtman G., Tzafriri L. Symmetric structures in Banach spaces. Mem. Amer. Math. Soc. 1979, 217.
  19. Johnson W.B., Odell E. Subspaces of $L_p$ which embed into $\ell_p$. Compos. Math. 1974, 28 (1), 37-49.
  20. Kadec M.I. On the linear dimension of the spaces $L_p$ and $\ell_q$. Uspekhi Mat. Nauk. 1958, 13 (6), 95-98. (in Russian)
  21. Kadec M.I., Pełczyński A. Bases, lacunary sequences and complemented subspaces in the spaces $L_p$. Studia Math. 1962, 21 (2), 161-176.
  22. Kalton N.J. Isomorphisms between $L_p$-function spaces when $p < 1$. J. Funct. Anal. 1981, 42 (3), 299-337.
  23. Lacey H.E. The Isometrical Theory of Classical Banach Spaces. Springer-Verlag, Berlin-Heidelberg-New York, 1974.
  24. Lévy. M. Prolongement d'un opérateur d'un sous-espace de $L^1(\mu)$ dans $L^1(\nu)$. Séminaire d'Analyse Fonctionnelle 1979-1980. Exposé 5. Ecole Polytechnique, Palaiseau, 1980.
  25. Levy. P. Theorie de l'addition de variable aleatoires. Gauthier-Villars, Paris, 1937.
  26. Lewis D.R., Stegall C. Banach spaces whose duals are isomorphic to $\ell_1(\Gamma)$. J. Funct. Anal. 1973, 12, 177-187.
  27. Lindenstrauss J., Pełczyński A. Absolutely summing operators in $L_p$-spaces and their applications. Studia Math. 1968, 29 (3), 275-326.
  28. Lindenstrauss J., Pełczyński A. Contribution to the theory of classical Banach spaces. J. Funct. Anal. 1971, 8 (2), 225-249.
  29. Lindenstrauss J., Rosenthal H.P. The ${\mathcal L}_p$ spaces. Israel J. Math. 1969, 7 (4), 325-349.
  30. Lindenstrauss J., Tzafriri L. Classical Banach spaces, Vol. 1, Sequence spaces. Springer-Verlag, Berlin-Heidelberg-New York, 1977.
  31. Lindenstrauss J., Tzafriri L. Classical Banach spaces, Vol. 2, Function spaces. Springer-Verlag, Berlin-Heidelberg-New York, 1979.
  32. Maharam D. On homogeneous measure algebras. Proc. Natl. Acad. Sci. USA 1942, 28, 108-111.
  33. Maslyuchenko O.V., Mykhaylyuk V.V., Popov M.M., A lattice approach to narrow operators. Positivity 2009, 13, 459-495.
  34. Maurey B. Sous-espaces compléméntes de $L^p$ d'apres P. Enflo. Semin. Maurey-Schwartz 1974-75, III, 1-14.
  35. Olevskii A.M. An orthonormal system and its applications. Math. Sb. (N.S.) 1966, 71 (113), 297-336. (in Russian)
  36. Paley R.E.A.C. A remarkable series of orthogonal functions. I. Proc. Lond. Math. Soc. 1932, 34, 241-264.
  37. Paley R.E.A.C. Some theorems on abstract spaces. Bull. Amer. Math. Soc. 1936, 42 (4), 235-240.
  38. Pełczyński A. Projections in certain Banach spaces. Studia Math. 1960, 19 (3), 209-228.
  39. Pełczyński A. On the impossibility of embedding of the space $L$ in certain Banach spaces. Colloq. Math. 1961, 8, 199-203.
  40. Pisier G. Complex interpolation and regular operators between Banach lattices. Arch. Math. (Basel) 1994, 62, 261-269.
  41. Popov M., Randrianantoanina B. Narrow Operators on Function Spaces and Vector Lattices. De Gruyter Studies in Mathematics 45, De Gruyter, Berlin-Boston, 2013.
  42. Rosenthal H.P. Projections onto translation-invariant subspaces of $L^p(G)$. Mem. Amer. Math. Soc. 1966, 63.
  43. Rosenthal H.P. On subspaces of $L^p \, (p > 2)$ spanned by sequences of independent random variables. Israel J. Math. 1970, 8 (3), 273-303.
  44. Rosenthal H.P. On subspaces of $L^p$. Ann. of Math. 1973, 97 (2), 344-373.
  45. Rosenthal H.P. Convolution by a biased coin. Altgeld Book (Univ. of Illinois) 1975-76, II.
  46. Rosenthal H.P. On an inequality of A. Grothendieck concerning operators on $L^p$. Positivity 1998, 2, 115-122.
  47. Schaefer H.H. Banach Lattices and Positive Operators. Springer-Verlag. Berlin-Heidelberg-New York, 1974.
  48. Schechtman G. Examples of $\mathcal L_p$-spaces} (1 < $ p \neq 2 $ < ∞). Israel J. Math. 1975, 22 (2), 138-147.
  49. Semenov E.M. Basis properties of the Olevskii system. Mat. Zametki 1993, 54 (3), 155-156. (in Russian) (translation of Math. Notes 1993, 54 (3-4), 977-978.)