An Isometry On Tensor Product Of C~*-Algebras

In this paper we study a condition which is called property(C′),namely an isometry on algebraic tensor products which are completed by the minimal C~*-norm. We show that property(C′)passes to the C~*-subalgebras and finite tensor products.It is also closed under the inductive limits.If the arbitrary tensor product is defined by the inductive limits of finite tensor products,then it satisfies property(C′).Finally,we study the relations between three similar properties.