Maps Preserving Operator Pairs Whose Products Or Jordan Triple Products Are Partial Isometries

The preserving problem is one of the most significant part of study of operator algebras.Partial isometries paly a vital role in von Neumann algebra.Preserving their algebra or geometry properties caught scholars both at home and abroad at-tention.Let B(H)be the set of all bounded linear operators.In this thesis,we obtain these results.1.Assume that ? is an additive surjective map on B(H).Then ? preserves nonzero partial isometries of products of two operators in both directions if and only if ? can be written in the following forms:there is a unitary operator or anti-unitary operator U on H and some constant ? with ??T,such that?(X)= ?UXU*,(?)X?B(H).2.Assume that ? is an additive surjective map on B(H).Then ? preserves nonzero partial isometries of Jordan triple products of two operators in both direc-tions if and only if there is a unitary operator or anti-unitary operator U on H and some constant ? with ? ? T,such that one of the following forms can be hold:(1)?(X)= ?UXU*,(?)X ? B(H);(2)?(X)= ?UX*U*,(?)X?B(H).