مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Information Journal Paper

Title

Schur multiplier operator and matrix inequalities

Pages

  383-390

Abstract

 In this note we obtain a reverse version of the Haagerup Theorem. In particular, if $ A \in \mathbb{M}_{n}$ has a $ 2\times2- $ principal submatrix as $ \left[ \begin{array}{cc}1& \alpha \\\beta & 1\\\end{array}\right]$ with $ \beta \neq \bar{\alpha}, $ then $ \Vert S_{A} \Vert > 1$ where the operator $ S_{A}:\mathbb{M}_{n}\longrightarrow \mathbb{M}_{n} $ is defined by $S_{A}(B) := A \circ B $ where $ "\circ " $ stands for Schur product.

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