On the distance coefficient between isomorphic function spaces

IfX, Y are compact countable metric spaces such thatY contains no subset homeomorphic toX, then for any isomorphismΦ ofC(X) intoC(Y), ‖ φ ‖ ‖ φ⁻¹ ‖≧3. This result and some variants of it are established here, and prove a special case of a conjecture raised in 1]. This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof. J. Lindenstrauss. I wish to thank Prof. Lindenstrauss and Prof. A. Dvoretzky for their guidance and the interest they showed in this work.