Countable projective spectra of countable inductive limits, called (PLB)-spaces, of weighted Banach spaces of continuous functions
are investigated. It is characterized when the derived projective limit functor vanishes in terms of the sequences of the
weights defining the spaces. The locally convex properties of the corresponding projective limits are analyzed, too.
Mathematics Subject Classification (2000). Primary 46E10 - Secondary: 46A13, 46M18, 46M40
Keywords. (PLB)-spaces - derived projective limit functor - weighted spaces of continuous functions
Dedicated to Professor Heinz König on the occasion of his 80th birthday
Received: 30 January 2009