Some New Notions of Bases for the Range of Operators in Hilbert Spaces - Hessam Hosseinnezhad (Sahand Communications in Mathematical Analysis)
This paper is devoted to introduce a new concept of bases for the range of the operator $K$. Actually, we consider controlled $K$-orthonormal and controlled $K$-Riesz bases which are a generalization of ordinary bases in Hilbert spaces. In the sequel, we give some characterizations of these  sequences. Next, we construct some new controlled bases with operator theory tools.  Finally, some dual characterizations are given.