On a problem of Rolewicz concerning separable quotients of F-spaces

• Autorzy: Wójtowicz, M.
• Języki publikacji: EN

Abstrakty

EN

Let Psi be a (nonconvex) Musielak-Orlicz function, and let (Omega, Sigma, mi) be a sigma-finite measure space. If L[psi] (mi) [is different from E[psi] (mi), where E[psi] (mi) is the space of the elements of L[psi] (mi) with absolutely continuous norm, then L[psi] (mi) has an infinite dimensional separable Banach quotient (Theorem).

Słowa kluczowe

PL

analiza funkcjonalna

EN

F-spaces; Musielak-Orlicz spaces; separable quotients of F-spaces; spaces of measurable functions

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 313--317
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Wójtowicz, M.

• Institute of Mathematics, Pedagogical University , Pl. Słowianski 9, 65-069 Zielona Góra, Poland

Bibliografia

• [1] C. D. Aliprantis, O. Burkinshaw, Locally Solid Riesz Spaces, Academic Press, New York 1978.
• [2] C. D. Aliprantis, O. Biirkinshaw, Positive Operators, Academic Press, New York 1985.
• [3] L. Drewnowski, A solution to a problem of De Wilde and :Tsiritinikov, Manuscripta Math., 37 (1982) 61-64.
• [4] M. A. Krasnoselskii, Ya. B, Rutickii, Convex Functions and Orlicz Spaces, P. Noordhof Ltd., Groningen 1961.
• [5] JI. E. Lacey, Separable quotients of Banach spaces, An. Acad. Bras. Cienc., 44 (1972) 185-189.
• [6] W. A. J. Luxemburg, A. C. Znane n, Riesz Spaces I, North Holland, Amsterdam 1971.
• [7] P. P. Narayanaswami, The separable quotient problem for barrelled spaces, in: Functional Analysis and Related Topics, 1991 (Kyoto). Springer-Verlag, Berlin (1993) 289-308.
• [8] M. Nowak, Singular linear functionals on non-locally convex Orlicz spaces, lndag. Mathem., N.S., 3 (1992) 337-351.
• [9] A. M. Plichko, M. M. Popov, Symmetric function spaces on atomless probability spaces, Dissert. Math., 306 (1990) 1-88.
• [10] M. M. Popov, On codimension of spaces LP (p) with O Kp< 1 (in Russian), Funktsional. Anal. Prilozhen., 18 (1984) 94-95.
• [11] S. Rolewicz, Metric Linear Spaces, Polish Scientific Publishers, Warszawa 1984.
• [12] H. P. Rosenthal, On quasicomplemented subspaces of Banach spaces with an appendix on compactness of operators from LP (u) to L"(v), J. Func. Anal., 4 (1969) 176-214.
• [13] W. Śliwa, M. Wójtowicz, Separable Quotients of Locally Convex Spaces, Bull. Pol. Ac.: Math., 43 (1995) 175-185.
• [14] W. Śliwa, (LF)-Spaces and the Separable Quotient Problem (Thesis, in Polish), Poznań 1996.
• [15] L. Weis, Perturbation Classes of Semi-Fredholm Operators, Math. Z., 178 (1981) 429-442.
• [16] W. Wnuk, On the order-topological properties of the quotient space LILA, Studia Math., 79 (1984) 139-149.
• [17] W. Wnuk, Representations of Orlicz lattices, Dissert. Math., 235 (1984) 1-66.
• [18] M. Wójtowicz, Effective constructions of separable quotients of Banach spaces, Collect. Math., 48 (1997) 809-815.
• [19] M. Wójtowicz, Acknowledgement of priority: Separable quotients of Banach spaces, Collect. Math., 49 (1998) 133-133.
• [20] H. Zhong, Some remarks related to the separable quotient problem, Acta Math. Sinica, 16 (1996) 248-256.