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1994 | 111 | 3 | 263-281
Tytuł artykułu

Coincidence of topologies on tensor products of Köthe echelon spaces

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EN
We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from $l_p$ to $l_q$. Several sharp forms of this result are also included.
Twórcy
autor
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain , mat6jbs0@cci.upv.es
autor
autor
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain , mat6apm@cci.upv.es
Bibliografia
  • [1] V. Bartík, K. John and J. Korbaš, Tensor products of operators and Horn's inequality, in: Oper. Theory: Adv. Appl. 14, Birkhäuser, Basel, 1984, 39-46.
  • [2] K. D. Bierstedt und R. Meise, Induktive Limiten gewichteter Räume stetiger und holomorpher Funktionen, J. Reine Angew. Math. 282 (1976), 186-220.
  • [3] K. D. Bierstedt, R. Meise and W. H. Summers, A projective description of weighted inductive limits, Trans. Amer. Math. Soc. 272 (1982), 107-160.
  • [4] K. D. Bierstedt, R. Meise and W. H. Summers, Köthe sets and Köthe sequence spaces, in: Functional Analysis, Holomorphy and Approximation Theory, North-Holland Math. Stud. 71, North-Holland, 1982, 27-91.
  • [5] B. Carl, B. Maurey und J. Puhl, Grenzordnungen von absolut-(r, p)-summierenden Operatoren, Math. Nachr. 82 (1978), 205-218.
  • [6] A. Defant, Barrelledness and nuclearity, Arch. Math. (Basel) 44 (1985), 168-170.
  • [7] A. Defant and K. Floret, Topological tensor products and the approximation property of locally convex spaces, Bull Soc. Roy. Sci. Liège 58 (1989), 29-51.
  • [8] A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, North-Holland, 1993.
  • [9] A. Defant and V. Mascioni, Limit orders of ε-π continuous operators, Math. Nachr. 145 (1990), 337-344.
  • [10] A. Defant and L. A. Moraes, On unconditional bases in spaces of holomorphic functions in infinite dimensions, Arch. Math. (Basel) 56 (1991), 163-173.
  • [11] S. Dineen and R. M. Timoney, Absolute bases, tensor products and a theorem of Bohr, Studia Math. 94 (1989), 227-234.
  • [12] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [13] H. Jarchow, Locally Convex Spaces, Teubner, 1981.
  • [14] H. Jarchow and K. John, On the equality of injective and projective tensor products, Czechoslovak Math. J. 38 (1988), 464-472.
  • [15] H. Jarchow and K. John, Bilinear forms and nuclearity, preprint, 1992.
  • [16] K. John, Counterexample to a conjecture of Grothendieck, Math. Ann. 265 (1983), 169-179.
  • [17] K. John, On the compact non-nuclear operator problem, ibid. 287 (1990), 509-514.
  • [18] G. Köthe, Topological Vector Spaces I, II, Springer, 1969, 1979.
  • [19] P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland Math. Stud. 131, North-Holland, 1987.
  • [20] A. Pietsch, Nuclear Locally Convex Spaces, Springer, 1972.
  • [21] A. Pietsch, Operator Ideals, Deutscher Verlag Wiss., 1978.
  • [22] A. Pietsch, Eigenvalues and s-Numbers, Cambridge University Press, 1987.
  • [23] G. Pisier, Counterexamples to a conjecture of Grothendieck, Acta Math. 151 (1983), 180-208.
  • [24] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Ser. in Math. 60, Amer. Math. Soc., 1986.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv111i3p263bwm
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