Linear Maps Preserving Quasi-Unitary Operators

Let H be a in nite separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. We give the concrete forms of surjec- tive linear maps : B(H) → B(H) preserving quasi-unitary operators and using this result for giving a form of when it preserves operator pairs whose products or triple Jordan products are nonzero quasi-unitary operators in both directions.