The Numerical Radius Haagerup Norm and Hilbert Space Square Factorizations
نویسندگان
چکیده
Abstract. We study a factorization of bounded linear maps from an operator space A to its dual space A∗. It is shown that T : A −→ A∗ factors through a pair of a column Hilbert spaces Hc and its dual space if and only if T is a bounded linear form on A ⊗ A by the canonical identification equipped with a numerical radius type Haagerup norm. As a consequence, we characterize a bounded linear map from a Banach space to its dual space, which factors through a pair of Hilbert spaces.
منابع مشابه
extend numerical radius for adjointable operators on Hilbert C^* -modules
In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.
متن کاملSome improvements of numerical radius inequalities via Specht’s ratio
We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...
متن کاملInequalities for the Norm and Numerical Radius of Composite Operators in Hilbert Spaces
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
متن کاملReverse Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
متن کاملOn the Numerical Radius of a Quaternionic Normal Operator
We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...
متن کامل