Let (A_1,||.||_1), (A,||.||), and (B,||.||) be commutative semisimple Banach algebras such that A_1\subset A. Let x be in A\tensor B (projective tensor product) such that \phi(x)\in A_1 for all \phi in the Gelfand space of A. Does it follow that x\in A_1 \tensor B(projective tensor product)?