Uncomplemented uniform algebras |
| |
Authors: | S V Kislyakov |
| |
Institution: | 1. Leningrad State University, USSR
|
| |
Abstract: | Let A be a closed subalgebra of the algebra of all complex-valued continuous functions on a compact space X, and suppose A contains the constant functions and separates points of X; let I be a closed ideal of A such that for some linear multiplicative functional ? on A we have the relation 0 > ∥?∣r∥ > 1 (for the existence of such an ideal it is sufficient that in the maximal ideal space of the algebra A there exists a Gleason part consisting of at least two points). Then the Banach space A** is not injective in particular, A is not a complemented subspace of C(X)]. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|