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Contributions to the theory of the classical Banach spaces. (English) Zbl 0224.46041


MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E15 Banach spaces of continuous, differentiable or analytic functions
46B25 Classical Banach spaces in the general theory
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References:

[1] Bessaga, C.; Pełczyński, A., On bases and unconditional convergence of series in Banach spaces, Studia Math., 17, 151-164 (1958) · Zbl 0084.09805
[2] Bessaga, C.; Pełczyński, A., Spaces of continuous functions IV, Studia Math., 19, 53-62 (1960) · Zbl 0094.30303
[3] Boas, R. P., Isomorphism between \(H_p\) and \(L_p\), Amer. J. Math., 77, 655-656 (1955) · Zbl 0065.34502
[4] Day, M. M., Normed linear spaces (1958), Berlin · Zbl 0082.10603
[5] Dunford, N.; Schwartz, J. T., Linear Operators I (1958), New York
[6] Ellis, H. W.; Halperin, I., Haar functions and the basis problem for Banach space, J. London Math. Soc., 31, 28-39 (1956) · Zbl 0070.33604
[7] James, R. C., Uniformly non-square Banach spaces, Ann. of Math., 80, 542-550 (1964) · Zbl 0132.08902
[8] Kwapień, S.; Pełczyński, A., The main triangle projection in matrix spaces and its application, Studia Math., 34, 43-68 (1970) · Zbl 0189.43505
[9] Lazar, A. J.; Lindenstrauss, J., Banach spaces whose duals are \(L_1\) spaces and their representing matrices, Acta Math., 126, 165-193 (1971) · Zbl 0209.43201
[10] Lindenstrauss, J., A short proof of Liapounoff’s convexity theorem, J. Math. and Mech., 15, 971-972 (1966) · Zbl 0152.24403
[11] Lindenstrauss, J., On complemented subspaces of \(m\), Israel J. Math., 5, 153-156 (1967) · Zbl 0153.44202
[12] Lindenstrauss, J.; Pełczyński, A., Absolutely summing operators in \(L_p\) spaces and their applications, Studia Math., 29, 275-326 (1968) · Zbl 0183.40501
[13] Lindenstrauss, J.; Rosenthal, H. P., Automorphisms in \(c_0, l_1\) and \(m\), Israel J. Math., 7, 227-239 (1969) · Zbl 0186.18602
[14] Michael, E.; Pełczyński, A., A linear extension theorem, Illinois J. Math., 11, 563-579 (1967) · Zbl 0171.10901
[15] Milman, V. P., The spectrum of bounded continuous functions defined on the unit sphere of a Banach space, Funktional. Anal. i Prilozen., 3, 67-79 (1969), (in Russian) · Zbl 0203.45001
[16] Milyutin, A. A., Isomorphism of spaces of continuous functions on compacta of the power continuum, Teoriya Funktsii Funkcional. Anal. i Prilozen Kharkov, 2, 150-156 (1966), (in Russian) · Zbl 0253.46050
[17] Mitiagin, B. S., An interpolation theorem for modular spaces, Mat. Sb., 66, 473-482 (1965), (in Russian) · Zbl 0142.10701
[18] Olevskii, A. M., Fourier series and Lebesgue functions, (Summary of a lecture to the Moscow Math. Soc.. Summary of a lecture to the Moscow Math. Soc., Usp., Mat. Nauk, 22 (1967)), 236-239, (in Russian)
[19] Pełczyński, A., Projections in certain Banach spaces, Studia Math., 19, 209-228 (1960) · Zbl 0104.08503
[20] Pełczyński, A., Linear extensions, linear averagings and their applications to linear topological classification of spaces of continuous functions, Rozprawy Mat., 58 (1968) · Zbl 0165.14603
[21] Pełczyński, A., On \(C(S)\) subspaces of separable Banach spaces, Studia Math., 31, 513-522 (1968) · Zbl 0169.15402
[22] Pełczyński, A.; Singer, I., On nonequivalent bases and conditional bases in Banach spaces, Studia Math., 25, 5-25 (1964) · Zbl 0187.05403
[23] Rosenthal, H. P., On the subspaces of \(L^p (p > 2)\) spanned by sequences of independent random variables, Israel J. Math., 8, 273-303 (1970) · Zbl 0213.19303
[24] Semadeni, Z., Banach spaces non isomorphic to their cartesian squares II, Bull. Acad. Polon. Sci., 8, 81-84 (1960) · Zbl 0091.27802
[25] Sierpiński, W., Cardinal and ordinal numbers, Monografie Mat. (1958) · Zbl 0083.26803
[26] Sobczyk, A., Projections of the space \(m\) on its subspace \(c_0\), Bull. Amer. Math. Soc., 47, 938-947 (1941) · JFM 67.1045.01
[27] Zakharyuta, V. P.; Yudovich, V. I., The general form of the linear functional in \(H_p\), Uspehi. Mat. Nauk., 19, 139-142 (1964), (in Russian) · Zbl 0128.34305
[28] A. L. Shields and D. L. Williams; A. L. Shields and D. L. Williams · Zbl 0227.46034
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