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Author(s):

**Javad Baradaran and Zahra Ghorbani**

Department of Mathematics,

Jahrom University, P.B. 7413188941,

Jahrom,

Iran.

E-mail:
baradaran@jahromu.ac.ir

Department of Mathematics,

Jahrom University, P.B. 7413188941,

Jahrom,

Iran.

E-mail: ghorbani@jahromu.ac.ir

Abstract:

In this paper, we first show the conditions under which an operator
on a Hilbert space *H* can be represented as sum of two unitary operators. Then, it is concluded that a Riesz
basis for a Hilbert space *H* can be written as a sum of two orthonormal bases. Finally, the study proves that if
*A* is a normal maximal partial isometry on a Hilbert space *H* and if
{e_{k}}^{∞}_{k=1} is an orthonormal
basis for *H*, then {Ae_{k}}^{∞}_{k=1}
is a 1-tight frame for *H*.

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