A Hausdorff Operator with Commuting Family of Perturbation Matrices Is a Non-Riesz Operator

The Operator Fejér-Riesz Theorem

The Fejér-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrixand operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum’s operator generalization of the classical Fejér-Riesz theorem. Mathematics Subject Classification (2000). Primary 47A68; Secondary 60G25, 47A56, 47B35, 42A05, 32A70, 30E99.

Operator Radii of Commuting Products

Operator radii wp(T) for a bounded linear operator T on a Hubert space were introduced in connection with unitary p-dilations. We shall be concerned with universal estimates for the ratios wp(ST)/(wa(S)wl,(T)) for commuting operators S, T and o, p > 0. 1. All operators in this paper are bounded linear operators on a complex Hubert space §. We say an operator T belongs to the class G (0 < p < oo...

Perturbation theory for Hamiltonian operator matrices and Riccati equations

Hypersurfaces of a Sasakian space form with recurrent shape operator

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.

Some properties of a general integral operator

In this paper‎, ‎we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $mathcal{S}^{*}(alpha),$ $mathcal{K}(alpha),$ $mathcal{M}(beta),$ $mathcal{N}(beta)$ and $mathcal{KD}(mu,beta).$‎