• Title, Summary, Keyword: quasinormal operator

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A NOTE ON k-HYPERREFLEXIVITY OF TOEPLITZ-HARMONIC SUBSPACES

  • Budzynski, Piotr;Piwowarczyk, Kamila;Ptak, Marek
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1727-1733
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    • 2014
  • The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an isometry or a quasinormal operator is shown. The k-hyperreflexivity of the tensor product $\mathcal{S}{\otimes}\mathcal{V}$ of a k-hyperreflexive decom-posable subspace $\mathcal{S}$ and an abelian von Neumann algebra $\mathcal{V}$ is established.

MAXIMUM SUBSPACES RELATED TO A-CONTRACTIONS AND QUASINORMAL OPERATORS

  • Suciu, Laurian
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.205-219
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    • 2008
  • 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.