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Tensor products and p-induction of representations on Banach spaces

  • Autores: William Moran, Philippe Jaming Árbol académico
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 51, Fasc. 1, 2000, págs. 83-110
  • Idioma: inglés
  • Enlaces
  • Resumen
    • In this paper we obtain $L^p$ versions of the classical theorems of induced representations, namely, the inducing in stages theorem, the Kronecker product theorem, the Frobenius Reciprocity theorem and the subgroup theorem. In doing so we adopt the tensor product approach of Rieffel to inducing.

  • Referencias bibliográficas
    • J.-Ph. Anker, Applications de la $p$-induction en analyse harmonique, Comment. Math. Helv. 58 (1983), 622–645.
    • S. Chevet, Sur certains produits tensoriels topologiques d’espaces de Banach, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 11 (1969), 120–138.
    • A. Defant and K. Floret, Tensor Norms and Operator Ideals, Number 176 in Mathematics Studies, North Holland, 1993.
    • J.M.G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472–476.
    • R.A. Fontenot and J.E. Schottenman, Induced representations of groups on Banach spaces, Rocky Mountain J. Math. 7 (1977), 53–82.
    • S.A. Gaal, Linear Analysis and Representation Theory, Number 198 in Grundlehren der Mathematischen Wissenschaften. Springer, 1973.
    • J. Glimm, Families of induced representations, Pacific J. Math. 12 (1962), 885–911.
    • Y. Gordon and P. Sahar, Ideal norms on $E \otimes L\_p$, Illinois J. Math. 21 (1977), 266–285.
    • A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
    • C. Herz, The theory of $p$-spaces with an application to convolution operators, Trans. Amer. Math. Soc. 154 (1971), 69–82.
    • E. Hewitt and K.A. Ross, Abstract Harmonic Analysis I, Number 115 in Grundlehren der mathematischen Wissenschaften. Springer, 1963.
    • H. Krajewic, Induced representations of groups on Banach spaces, Glas. Math. Ser. III 4 (1969), 183–196.
    • S. Kwapień, On operators factorizable through $L\_p$-spaces, Bull. Soc. Math. France, memoire 31-32 (1972), 15–225.
    • J. Lindenstrauss and A. Pelczynski, Absolutely summing operators in $L\_p$-spaces and their applications, Studia Math. 29 (1968), 275–326.
    • Y.I. Lyubich, Introduction to the Theory of Banach Representations of Groups, Operator Theory: Advances and Applications 30, Birkhäuser, 1988.
    • G. Mackey, Induced representations of locally compact groups I, Ann. of Math. (2) 55 (1952), 101–140.
    • G. Racher, Remarks on a paper of Bachelis and Gilbert, Monatsh. Math. 92 (1981), 47–60.
    • H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford Mathematical Monographs, 1968.
    • M.A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Func. Anal. 1 (1967), 443–491.
    • M.A. Rieffel, Unitary representations induced from compact groups, Studia Math. 42 (1972), 145–175.
    • P. Sahar, Applications $p$-sommantes et $p$-décomposantes, C. R. Acad. Sci. Paris Sér. A-B 270 (1969), 528–531.
    • J.E. Schottenman, Integral operators in the theory of induced Banach representations, Mem. Amer. Math. Soc. 207 (1978).

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