Given commuting d-tuples S i and T i , 1 ≤ i ≤ 2, Banach space operators such that the tensor products pair (S 1 ⊗ S 2 , T 1 ⊗ T 2 ) is strict m-isometric (resp., S 1 , S 2 are invertible and (S 1 ⊗ S 2 , T 1 ⊗ T 2 ) is strict m-symmetric), there exist integers m i > 0, and a non-zero scalar c, such that m = m 1 + m 2 − 1, (S 1 , 1 c T 1 ) is strict m 1 -isometric and (S 2 , cT 2 ) is strict m 2 -isometric (resp., there exist integers m i > 0, and a non-zero scalar c,