대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제15권4호
  • /
  • Pages.617-626
  • /
  • 2000
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

LINEAR FUCTIONALS ON $O_n$ ASSOCIATED TO UNIT VECTORS

  • 발행 : 2000.10.01
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초록

We study the vectors related tro states on the Cuntz algebra Ο(sub)n and prove hat, for tow states $\omega$ and $\rho$ on Ο(sub)n with $\omega$│UHF(sub)n = $\rho$│UHF(sub)n, if ($\omega$(s$_1$), …, $\omega$(s(sub)n)) and ($\rho$(s$_1$),…, $\rho$(s(sub)n)) are unit vectors, then they and linearly dependent. We also study the linear functional on Ο(sub)n associated to a sequence of unit vectors in C(sup)n which is the generalization of the Cuntz state. We show that if the linear functional associated to a sequence of unit vectors with a certain condition is a state, then it is just the Cuntz state.

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참고문헌

  1. Integral Equations Operator Theory v.28 Isometries, Shifts, Cuntz Algebras and mutiresolution wavelet analysis of sale N O. Bratteli;P.E.T. Jorgensen
  2. Proc. Sympos. Pure Math. v.59 Endomorphisms of B(H) O. BRATTELI;P.E.T. Jorgensen;H.L. Price
  3. Comm. Math. Pys. v.57 Simple C* -algebras generated by isometries J. Cuntz
  4. Trans. Ame. Math. Soc. v.95 On a certain calss of operator algebras J. Glimm
  5. Proc. Amer. Math.Soc. v.127 Irreducible representation of the Cuntz algebra E.C. Jeong
  6. Ann. Math v.86 Representations of uiformly hyperfinite algebras and their associated von Neumann rings R.T. Powers