Related topics on Operator Theory and Operator Algebras

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Our interest of this research is in the intersection area of Operator Theory and Operator Algebra.One of main results is to characterize the numerical radius norm of Schur multipiers. U.Haagerup refound the characterization of the norm of Schur multiplier and he constructed the theory of Haagerup tensor product of operator spaces. T.Ando proved the similar characterization of the numerical radius norm of Schur multipliers for matrices. Our result is extended vesion of Ando's result.Next result is concerned with operator spaces. As an application of abobe result, we consider linear spaces with matrix norms. Usual norms implies the structure of operator spaces. We consider numerical radius norms instead of usual norms. We call it numerical radius operator space. Z.-J.Ruan proved that every operator spaces can be realized as a subspace of B(H) with usual norms, where B(H) is the set of all bounded linear operators on a Hilbert space H. We can show the similar result for numerical radius operator spaces, that is, every numerical radius operator spaces can be realized as a subspace of B(H) with numerical radius norms. This result contains Ruans' result as a special case.