Norm and Numerical Radius Inequalities for a Product of Two Linear Operators in Hilbert Spaces
نویسنده
چکیده
The main aim of the present paper is to establish some norm and numerical radius inequalities for the composite operator BA under suitable assumptions for the transform Cα,β (T ) := (T ∗ −αI) (β I−T ) , where α ,β ∈ C and T ∈ B(H), of the operators involved. Mathematics subject classification (2000): Primary 47A12, 47A30; Secondary 47A63..
منابع مشابه
Some 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 کاملextend 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 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 کاملSome Inequalities for (α, Β)-normal Operators in Hilbert Spaces
An operator T is called (α, β)-normal (0 ≤ α ≤ 1 ≤ β) if αT ∗T ≤ TT ∗ ≤ βT ∗T. In this paper, we establish various inequalities between the operator norm and its numerical radius of (α, β)-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.
متن کاملSOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS
In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...
متن کامل