Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON UDL DECOMPOSITIONS IN SEMIGROUPS

  • Lim, Yong-Do (Department of Mathematics Kyungpook National University )
  • Published : 1997.08.01
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Abstract

For a non-degenerate symmetric bilinear form $\sigma$ on a finite dimensional vector space E, the Jordan algebra of $\sigma$-symmetric operators has a symmetric cone $\Omega_\sigma$ of positive definite operators with respect to $\sigma$. The cone $C_\sigma$ of elements (x,y) \in E \times E with \sigma(x,y) \geq 0$ gives the compression semigroup. In this work, we show that in the sutomorphism group of the tube domain over $\Omega_\sigma$, this semigroup has a UDL and Ol'shanskii decompositions and is exactly the compression semigroup of $\Omega_sigma$.

Keywords

References

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