Concave Weighted Shift Operators and It's Hypercyclicity

Concave Weighted Shift Operators and It's Hypercyclicity

A bounded linear operator T on a Hilbert space H is concave, if for each x 2 H; kTxk2 􀀀 2kTxk2 + kxk2  0. In this study, it is shown that if T is a concave operator then It is injective. Also, observe that the only concave bilateral weighted shifts are isometries. Finally we show that no concave weighted shift operators is hypercyclic.