대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제18권1호
  • /
  • Pages.59-63
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  • 2003
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A NEW PROOF OF MACK'S CHARACTERIZATION OF PCS-ALGEBRAS

  • 발행 : 2003.01.01
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초록

Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.

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참고문헌

  1. Duke Math. J. v.40 Complications of semicontinuity in $C^*$-algebra theory C. A. Akemann;G. K. Pedersen https://doi.org/10.1215/S0012-7094-73-04070-2
  2. Proc. Amer. Math. Soc. v.9 On Properties characterizing pseudo-compact spaces R. W. Bagley;E. H. Connel;J. D. McKnight, Jr. https://doi.org/10.2307/2033015
  3. Canad. J. Math. v.40 Semicontinuity and multipliers of $C^*$-algebras L. G. Brown https://doi.org/10.4153/CJM-1988-038-5
  4. Memoirs Amer. Math. Soc. v.169 Multipliers of Pedersen's ideal A. J. Lazar;D. C. Taylor
  5. The spectrum of a PCS-algebra J. Mack
  6. Duke Math. J. v.22 Applications of weak semicontinuity in $C^*$-algebra theory G. K. Pedersen
  7. $C^*$-algebras and their automorphism groups G. K. Pedersen
  8. Proc. Amer. Math. Soc. v.104 A new approach to the multipliers of Pedersen's ideal N. G. Phillips https://doi.org/10.2307/2046807