Associated with T = U|T | (polar decomposition) in L(H) is a related operator T̃ = |T | 1 2U|T | 1 2 , called the Aluthge transform of T . In this paper we study some connections betweenT and T̃ , including the following relations; the single valued extension property, an analogue of the single valued extension property onWm(D,H), Dunford’s property (C) and the property (β). 2000 Mathematics Subj...

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

let $(m^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the sasakian space form$widetilde{m}(c)$. we show that if the shape operator $a$ of $m$ isrecurrent then it is parallel. moreover, we show that $m$is locally a product of two constant $phi-$sectional curvaturespaces.

Let L(H) denote the C∗-algebra of adjointable operators on a Hilbert C∗-module H. In this paper, we introduce generalized Cauchy–Schwarz inequality for in L(H). More precisely, an operator A∈L(H) is said to satisfy if there exists ν∈(0,1) such that ‖⟨Ax,y⟩‖≤(‖Ax‖‖y‖)ν(‖Ay‖‖x‖)1−ν(x,y∈H).We investigate various properties which inequality. particular, prove A satisfies has polar decomposition, th...