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References
Alexits, G.: Convergence problems of orthogonal series. New York: Pergamon Press 1961
Bennett, G.: Tensor products of l p spaces. Notices Amer. Math. Soc. 21, A-309 (1974)
Bennett, G.: Unconditional convergence and almost everywhere convergence. Notices Amer. Math. Soc. 21, A-488 (1974)
Bennett, G.: Some ideals of operators on Hilbert space. (To appear in Studia Math.)
Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
Day, M. M.: Normed linear spaces. 3rd ed., Berlin, Heidelberg, New York: Springer 1973
Erdös, P.: On the convergence of trigonometric series. J. Math. Phys. 22, 37–39 (1943)
Gapoškin, V. F.: Lacunary series and independent functions. Russian Math. Surveys 21, 1–82 (1966)
Garsia, A. M.: Combinatorial inequalities and convergence of some orthonormal expansions. Proc. Conf. Orthogonal Expansions, Southern Illinois University Press, Carbondale p. 75–92, 1968
Gordon, Y., Lewis, D. R.: Absolutely summing operators and local unconditional structures. Acta Math. 133, 27–48 (1974)
Hobson, E. W.: On the convergence of series of orthogonal functions. Proc. Lond. Math. Soc. 12, 297–308 (1913)
Jerosch, F., Weyl, H.: über die Konvergenz von Reihen, die nach periodischen Funktionen fortschreiten. Math. Ann. 66, 67–80 (1909)
Kantorovič, L.: Some theorems on the almost everywhere convergence. Dokl. Akad. Nauk USSR 14, 537–540 (1937)
Kwapien, S., Pelczynski, A.: The main triangle projection in matrix spaces and its applications. Studia Math. 34, 43–68 (1970)
Lorentz, G. G.: Riesz method of summation and orthogonal series. Trans. Roy. Soc. Canad. 45, 19–32 (1951)
Maurey, B., Nahoum, A.: Applications radonifantes dans l'espaces des séries convergentes. C. R. Acad. Sci. Paris Sér. A-B, 276, 751–754 (1973)
Mensov, D.: Sur les séries de fonctions orthogonales I, II. Fund. Math. 4, 82–105 (1923), and 10, 375–420 (1927)
Mitiagin, B. S., Pelczynski, A.: Nuclear operators and approximative dimension. Proc. Int. Cong. Math., Moscow 1966
Orlicz, W.: Zur Theorie der Orthogonalreihen. Bull. Int. Acad. Sci. Polon. 81–115 (1927)
Orlicz, W.: über unbedingte Konvergenz in FunktionenrÄumen (I). Studia Math. 4, 33–37 (1933)
Pietsch, A.: Absolut p-summierende Abbildungen in normierten RÄumen. Studia Math. 28, 333–352 (1967)
Pietsch, A.: Nukleare lokalkonvexe RÄume. Berlin: Akademie 1969
Plancherel, M.: Sur la convergence des séries de functions orthogonales. C. R. Acad. Sci. Paris Ser. A-B, 157, 539–542 (1913)
Rademacher, H.: Einige SÄtze über Reihen von allgemeinen Orthogonalfunktionen. Math. Ann. 87, 112–138 (1922)
Révész, P.: The laws of large numbers. New York: Academic Press 1968
Riesz, M.: Sur les fonctions conjuguées. Math. Z. 27, 218–244 (1927)
Salem, R.: A new proof of a theorem of Menchoff. Duke Math. Jour. 8, 269–272 (1941)
Schwartz, L.: Probabilités cylindriques et applications radonifantes. J. Fac. Sci. Univ. Tokyo 18, 139–285 (1971–72)
Stout, W. F.: Almost sure convergence. New York: Academic Press 1974
Sunouchi, G., Yano, S.: Convergence and summability of orthogonal series. Proc. Acad. Japan 26, 10–16 (1950)
Tandori, K.: über die orthogonalen Funktionen I. Acta Sci. Math. 18, 57–130 (1957)
Tong, A. E.: Diagonal submatrices of matrix maps. Pacific J. Math. 32, 551–559 (1970)
Weyl, H.: über die Konvergenz von Reihen, die nach Orthogonalfunktionen fortschreiten. Math. Ann. 67, 225–245 (1909)
Wojtaszczyk, P.: Approximation properties and universal Banach spaces. Colloq. Anal. Fonctionn. Bull. Math. Soc. France 31–32, 395–398 (1972)
Zygmund, A.: Trigonometrie series I, Cambridge: Cambridge University Press 1958
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Bennett, G. Unconditional convergence and almost everywhere convergence. Z. Wahrscheinlichkeitstheorie verw Gebiete 34, 135–155 (1976). https://doi.org/10.1007/BF00535681
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DOI: https://doi.org/10.1007/BF00535681