Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE SEPARATING IDEALS OF SOME VECTOR-VALUED GROUP ALGEBRAS

  • Garimella, Ramesh V. (Department of Mathematics, Tennessee Technological University)
  • Published : 1999.11.01
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Abstract

For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

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References

  1. J. Funct. Anal. v.29 Print ideals and automatic continuty for Banach algebras W. G. Bade;P. C. Curtis, Jr.
  2. Proceedings, Long Beach Derivations on commutative Banach algebras P. C. Curtis Jr.
  3. J. London Math. v.16 Automatic continuity and topologically simple radical Banach algebras J. Cusack
  4. Bull. London Math. Soc. v.10 Automatic continuity: A survey H. G. Dales
  5. Math surveys, Amer. Math. Soc. v.15 Vector measures J. Diestel;J. J. Uhl
  6. Proc. Amer. Math. Soc. v.117 On nilpotency of the separating ideal of a derivation R. Garimella
  7. Bull. Austral. Math. Soc. v.56 On continuity of derivations and epimorphisms on some vector-valued goups algebras R. Garimella
  8. Pacific J. Math. v.7 The Tauberian Theorem for Group algebras of vector-valued functions A. Hausner
  9. Trans. Amer. Math. Soc. v.92 Space of function with values in a Banach algebra G. P. Johnson
  10. Surveys and recent results Ⅱ, North-Holland Math. Studies v.38 Automatic continuity of linear operations in functional analysis M. M. Neumann
  11. Arch. Math. (Basel) v.68 no.2 Continuity of epimorphisms and derivations on vector-valued groups algebras M. M. Neumann;M. V. Velasco
  12. Fourier analysis on groups W. Rudin
  13. Lecture Notes Series v.21 Automatic continuity on linear operators A. M. Sinclair
  14. Lecture Note in Math. v.975 P. C. Curtis Jr.