Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 4 4 2016 8 31 On k-Quasi Class Q* Operators 87 91 EN Valdete Rexh?beqaj Hamiti Faculty of Electrical and Computer Engineering, University of Prishtina, Prishtin?, Kosova Shqipe Lohaj Qefsere Gjonbalaj TJANT2016441 10.12691/tjant-4-4-1 2016 4 15 2016 7 14 2016 8 29 Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class of operators: k-quasi class Q* operators. An operator T is said to be k-quasi class Q* if it satisfies for all xH, where k is a natural number. We prove the basic properties of this class of operators.