Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MAXIMUM SUBSPACES RELATED TO A-CONTRACTIONS AND QUASINORMAL OPERATORS

  • Suciu, Laurian (Institut Camille Jordan Universite Claude Bernard Lyon 1)
  • Published : 2008.01.31
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Abstract

It is shown that if $A{\geq}0$ and T are two bounded linear operators on a complex Hilbert space H satisfying the inequality $T^*\;AT{\leq}A$ and the condition $AT=A^{1/2}TA^{1/2}$, then there exists the maximum reducing subspace for A and $A^{1/2}T$ on which the equality $T^*\;AT=A$ is satisfied. We concretely express this subspace in two ways, and as applications, we derive certain decompositions for quasinormal contractions. Also, some facts concerning the quasi-isometries are obtained.

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References

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