On Automatic Continuity and Three Problems of "The Scottish Book" Concerning the Boundedness of Polynomial Functionals

Journal of Mathematical Analysis and Applications

Volumn 220, Issue 2, 1998, Pages 477-494

  Plichko, Anatolij ^a   Zagorodnyuk, Andriy ^b  

^a Kirovograd State Pedagogical University   (Ukraine)

^b Institute for Applied Problems of Mechanics and Mathematics   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040088810     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5826     Document Type: Article

References (27)

1. Alexiewicz A. On sequences of operations 1. Studia Math. 11:1950;1-30.
2. Auerbach H. Un théorème sur les polynomes àn. Studia Math. 5:1934;171-173.
3. Banach S. Théorème sur les ensembles de première categorie. Fund. Math. 16:1930;395-398.
4. Banach S. Théorie des opérations linéaires. 1932;Monografie Matematyczne, Warszawa.
5. Dineen S. Complex Analysis in Locally Convex Spaces. 1981;North-Holland, Amsterdam.
6. Druzkowski L. M. Two criteria for continuity of polynomials andG. Univ. Iagel. Acta Math. 24:1984;135-138.
7. Dunford N. On continuous mappings. Ann. of Math. 41:1940;639-661.
8. Fernandez C. S. The closed graph theorem for multilinear mappings. J. Math., Math. Sci. Internat. 19:1996;407-408.
9. Gajda Z. Christensen measurability of polynomial functions and convex functions of higher order. Ann. Polon. Math. 47:1986;25-40.
10. Hille E., Phillips R. S. Functional Analysis and Semi-Groups. Amer. Math. Soc. Colloq. Publ. 37:1957;Amer. Math. Soc. Providence.
11. Horowitz Ch. An elementary counterexample to the open mapping principle for bilinear maps. Proc. Amer. Math. Soc. 53:1975;293-294.
12. Kohen P. J. A counterexample to the Closed Graph Theorem for bilinear maps. J. Funct. Anal. 16:1974;235-240.
13. Köthe G. Stanislaw Mazur's contributions to functional analysis. Math. Ann. 277:1987;489-528.
14. Kuratowski K. Topology. 1966;Academic Press, New York.
15. Lindenstrauss J., Tzafriri L. Classical Banach Spaces, I. 1977;Springer-Verlag, Berlin.
16. Mazur S., Orlicz W. Grundlegende Eigenschaften der polynomischen Operationen I, II. Studia Math. 5:1934;50-68.
17. McShane E. J. Images of sets satisfying the conditions of Baire. Ann. of Math. 51:1950;380-386.
18. V. Pestov, Two 1935 questions of Mazur about polynomials in Banach spaces: A Counter-example.
19. Pettis B. J. On continuity and openness of homomorphisms in topological groups. Ann. of Math. 52:1950;293-308.
20. Petunin Yu. I., Plichko A. M. The Characteristic Theory of Subspaces and Its Applications. 1980;Vyshcha Shkola, Kyiv.
21. Petunin Yu. I., Savkin V. I. Continuity of inverse mappings to quadratic operator polynomials. Ukrain. Mat. Zh. 41:1989;1512-1521.
22. Plichko A. M. Bases and complements in nonseparable Banach spaces. Sibirsk. Mat. Zh. 25:1984;155-162.
23. Pombo D. P. Jr. On a result due to Nachbin. C. R. Acad. Bulgare Sci. 44:1991;5-6.
24. Rolewicz S. On inversion of non-linear transformations. Studia Math. 17:1958;79-83.
25. r(ν). J. Funct. Anal. 4:1968;176-214.
26. Mauldin R. D. The Scottish Book. 1981;Birkhäuser, Boston.
27. Sinclair A. M. Automatic continuity of linear operators. London Math. Soc. Lecture Note Ser. 21:1976;Cambridge Univ. Press, Cambridge. p. 1-92.