Prof. dr. Garth Dales: Large fields and algebras of continuous functions
Date of publication: 12. 4. 2013
Mathematics colloquium
Četrtek, 18. 4. 2013, ob 18:15 v predavalnici 2.02 na Jadranski 21.
Garth Dales
Lancaster University, VB
We introduce the following question of Kaplansky: Let K be a compact space, and let C(K) denote the Banach algebra of all continuous functions on K. Are are all homomorphisms from C(K) into a Banach algebra automatically continuous?
We answer this by introducing some `large' totally ordered fields, and thinking whether the finite elements of these fields are normable. The only prerequisites for the talk are the knowledge that the real line is a totally ordered field that is Dedekind complete, and an awareness of the Continuum Hypothesis.
Full details of the proofs are contained in the following books:
H. G. Dales, Banach algebras and automatic continuity, OUP, 2001.
H. G. Dales and W. H. Woodin, Super-real fields: totally ordered fields with additional structure, OUP, 1996.
