Polar Decomposition For The Sum Of Two Operators

Let H and K be complex Hilbert spaces,and let the polar decompositions of T?B(H,K)and S?B(H,K)be T=U|T| and S=V|S| respectively.Under certain conditions,this paper gives the polar decomposition of T+S is T+S=(U+V)(|T|+|S|).In addition,the related corollaries of polar decomposition of EP operator and positive operator are obtained and examples are given.