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On Amenability in Banach algebras of Approximable Operators

O.T. Mewomo
장전수학회 (Jangjeon Mathematical Society)|2010.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제13권 제1호|pp. 17-30|DOI 10.17777/pjms.2010.13.1.003

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참고문헌

키워드

Banach algebraAmenabilityBanach spacebounded derivationproperty (A)tight tensor productaproximable operators
주제분류수학

초록

We give conditions for the Banach algebra of approximable operators on the injective tensor product between a Banach space and its dual to be amenable. In particular, we show that if dimX < ∞ and X∗ has property (A), then A((Xˇ⊗X∗)∗)and A(Xˇ⊗X∗) are both amenable. We also extend the results of the authors in [4].

Abstract

We give conditions for the Banach algebra of approximable operators on the injective tensor product between a Banach space and its dual to be amenable. In particular, we show that if dimX < ∞ and X∗ has property (A), then A((Xˇ⊗X∗)∗)and A(Xˇ⊗X∗) are both amenable. We also extend the results of the authors in [4].

참고문헌 (13)

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  2. A. Defant, "Tensor norms and operator ideals" (1993), North-Holland
  4. N. Gronbaek, "Amenability of Banach algebras of compact operators", Isreal J. Math., 87, pp.289~324 (1994)
  5. U. Haagerup, "All nuclear C＊-algebras are amenable", Invent. Math, 74, pp.305~319 (1983)
  6. B.E. Johnson, "Cohomology in Banach algebras", Mem. Amer. Math. Soc, 127 (1972)
  7. B.E. Johnson, "Weak amenability of group algebras", Bull. London Math. Soc, 23 (1991)
  8. S. Kwapien, "On operators factoring through Lp-space", Bull. Soc. Math. France, Mem, 31, pp.215~225 (1972)
  9. O.T. Mewomo, "Oguntuase, On property (Pλ) and weak amenability of A(X)", AL.I Cuza” DIN IASI (S.N) Mathematica, Tomul LIII, pp.85~96 (2007)
  10. T.W. Palmer, "Banach algebras and the general theory of *-algebras" (1994), Cambridge University Press
  11. J.R. Retherford, "Operator characterizations of Lp-spaces", Isreal J. Math., 13, pp.336~347 (1972)
  12. V. Runde, "Lectures on Amenability, Lect. Notes in Mathematics" (2002), Springer Verlag

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