Rosenthal L∞-theorem revisited

• Lech Drewnowski ^[1]
  1. [1] Adam Mickiewicz University. Polonia
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 36, Nº 2, 2021, págs. 147-155
• Idioma: inglés
• DOI: 10.17398/2605-5686.36.2.147
• Enlaces
  • Texto completo
• Resumen

  • A remarkable Rosenthal L∞-theorem is extended to operators T : L∞(Γ, E) → F , where Γ is an infinite set, E a locally bounded (for instance, normed or p-normed) space, and F any topological vector space.

• Referencias bibliográficas
  • [1] S.A. Argyros, J.M.F. Castillo, A.S. Granero, M. Jimenez- Sevilla, J.P. Moreno, Complementation and embeddings of c0(I) inBanach spaces,...
  • [2] C. Constantinescu, “ Spaces of Measures ”, De Gruyter Studies in Mathe-matics 4, Walter de Gruyter & Co., Berlin, 1984.
  • [3] L. Drewnowski, Un th ́eor`eme sur les op ́erateurs de `∞(Γ), C.R. Acad. Sci. Paris S ́er. A 281 (1975), 967 – 969.
  • [4] L. Drewnowski, An extension of a theorem of Rosenthal on operators acting from `∞(Γ), Studia Math. 57 (1976), 209 – 215.
  • [5] L. Drewnowski, Generalized limited sets with applications to spaces of type `∞(X) and c0(X), European J. Math. (to appear).
  • [6] L. Drewnowski, I. Labuda, Copies of c0and `∞ in topological Riesz spaces, Trans. Amer. Math. Soc. 350 (1998), 3555 – 3570.
  • [7] L. Drewnowski, I. Labuda, Topological vector spaces of Bochner measur- able functions, Illinois J. Math. 46 (2002), 287 – 318.
  • [8] N.J. Kalton, Exhaustive operators and vector measures, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), 291 – 300.
  • [9] N.J. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267 – 278.
  • [10] N.J. Kalton, N.T. Peck, J.W. Roberts, “ An F-space sampler ”, Lon- don Mathematical Society Lecture Note Series, 89, Cambridge UniversityPress,...
  • [11] J. Kupka, A short proof and a generalization of a measure theoretic disjoin- tization lemma, Proc. Amer. Math. Soc. 45 (1974), 70 – 72.
  • [12] I. Labuda, Sur les mesures exhaustives et certaines classes d’espaces vectorielstopologiques consid ́er ́es par W. Orlicz et L. Schwartz,...
  • [13] I. Labuda, Exhaustive measures in arbitrary topological vector spaces, Studia Math. 58 (1976), 239 – 248.
  • [14] A. Avil ́es, F. Cabello S ́anchez, J.M.F. Castillo, M. Gonz ́alez, Y. Moreno, “ Separably Injective Banach Spaces ”, Lecture Notes in...
  • [15] Z. Lipecki, The variation of an additive function on a Boolean algebra, Publ. Math. Debrecen 63 (2003), 445 – 459.
  • [16] S. Rolewicz, “ Metric Linear Spaces ”, Second edition, PWN`uPolish Scientific Publishers, Warsaw; D. Reidel Publishing Co., Dordrecht,...
  • [17] H.P. Rosenthal, On complemented and quasi-complemented subspaces of quotients of C(S) for stonian S, Proc. Nat. Acad. Sci. U.S.A. 60...
  • [18] H.P. Rosenthal, On relatively disjoint families of measures, with some ap- plications to Banach space theory, Studia Math. 37 (1970),...