PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 69 | 3 | 235-249
Tytuł artykułu

The intersection convolution of relations and the Hahn-Banach type theorems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an extension to a total linear selection.
Twórcy
  • Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf. 12, Hungary
Bibliografia
  • [1] J. Abreu and A. Etchebery, Hahn-Banach and Banach-Steinhaus theorems for convex processes, Period. Math. Hungar. 20 (1989), 289-297.
  • [2] R. Arens, Operational calculus of linear relations, Pacific J. Math. 11 (1961), 9-23.
  • [3] G. Buskes, The Hahn-Banach Theorem surveyed, Dissertationes Math. 327 (1993).
  • [4] J. Dieudonné, History of Functional Analysis, North-Holland Math. Stud. 49, North-Holland, Amsterdam, 1981.
  • [5] B. Fuchssteiner und J. Horváth, Die Bedeutung der Schnitteigenschaften beim Hahn-Banachschen Satz, Jahrbuch Überblicke Math. (BI, Mannheim) 1979, 107-121.
  • [6] B. Fuchssteiner and W. Lusky, Convex Cones, North-Holland Math. Stud. 56, North-Holland, Amsterdam, 1981.
  • [7] Z. Gajda, A. Smajdor and W. Smajdor, A theorem of the Hahn-Banach type and its applications, Ann. Polon. Math. 57 (1992), 243-252.
  • [8] G. Godini, Set-valued Cauchy functional equation, Rev. Roumaine Math. Pures Appl. 20 (1975), 1113-1121.
  • [9] D. B. Goodner, Projections in normed linear spaces, Trans. Amer. Math. Soc. 69 (1950), 89-108.
  • [10] M. Hasumi, The extension property of complex Banach spaces, Tôhoku Math. J. 10 (1958), 135-142.
  • [11] L. Holá and P. Maličký, Continuous linear selectors of linear relations, Acta Math. Univ. Comenian. 48-49 (1986), 153-157.
  • [12] J. Horváth, Some selected results of professor Baltasar Rodrí guez-Salinas, Rev. Mat. Univ. Complut. Madrid 9 (1996), 23-72.
  • [13] O. Hustad, A note on complex 𝓟₁ spaces, Israel J. Math. 16 (1973), 117-119.
  • [14] A. W. Ingleton, The Hahn-Banach theorem for non-Archimedean-valued fields, Proc. Cambridge Philos. Soc. 48 (1952), 41-45.
  • [15] A. D. Ioffe, A new proof of the equivalence of the Hahn-Banach extension and the least upper bound properties, Proc. Amer. Math. Soc. 82 (1981), 385-389.
  • [16] J. L. Kelley, Banach spaces with the intersection property, Trans. Amer. Math. Soc. 72 (1952), 323-326.
  • [17] J. L. Kelley, General Topology, Van Nostrand Reinhold, New York, 1955.
  • [18] S. Mac Lane, Homology, Springer, Berlin, 1963.
  • [19] L. Nachbin, A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28-46.
  • [20] K. Nikodem, Additive selections of additive set-valued functions, Zb. Rad. Prirod.-Mat. Fak. Univ. u Novom Sadu Ser. Mat. 18 (1988), 143-148.
  • [21] Zs. Páles, Linear selections for set-valued functions and extension of bilinear forms, Arch. Math. (Basel) 62 (1994), 427-432.
  • [22] B. Rodríguez-Salinas and L. Bou, A Hahn-Banach theorem for arbitrary vector spaces, Boll. Un. Mat. Ital. 10 (1974), 390-393.
  • [23] W. Smajdor, Subadditive and subquadratic set-valued functions, Prace Nauk. Uniw. Śląsk. Katowic. 889 (1987), 73 pp.
  • [24] W. Smajdor and J. Szczawińska, A theorem of the Hahn-Banach type, Demonstratio Math. 28 (1995), 155-160.
  • [25] T. Strömberg, The operation of infimal convolution, Dissertationes Math. 352 (1996).
  • [26] Á. Száz, Pointwise limits of nets of multilinear maps, Acta Sci. Math. (Szeged) 55 (1991), 103-117.
  • [27] Á. Száz, Foundations of Linear Analysis, Inst. Mat. Inf., Lajos Kossuth University Debrecen 1996, 200 pp. (Unfinished lecture notes in Hungarian).
  • [28] Á. Száz and G. Száz, Additive relations, Publ. Math. Debrecen 20 (1973), 259-272.
  • [29] Á. Száz and G. Száz, Linear relations, Publ. Math. Debrecen 27 (1980), 219-227.
  • [30] J. Zowe, Sandwich theorems for convex operators with values in an ordered vector space, J. Math. Anal. Appl. 66 (1978), 282-396.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv69z3p235bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.