Main Article Content
On contractibility of matrix algebras
Abstract
We show first that for each C*algebra
A, contractibility of A implies
contractibility of Mn(A).
We next prove that an incidence algebra A of upper
triangular matrices, defined by a partially ordered set Ω on {1, 2,...,
n}
satisfying (p, q) ∈ Ω ⇒ p ≤ q, is a contractible
Banach
algebra if there is no discordant coupled of D-transitive triples of elements
of Ω.
Mathematics Subject
Classification (2000):
Primary 46H05, 46H25; Secondary 15A99
Quaestiones Mathematicae 25 (2002), 327-332
A, contractibility of A implies
contractibility of Mn(A).
We next prove that an incidence algebra A of upper
triangular matrices, defined by a partially ordered set Ω on {1, 2,...,
n}
satisfying (p, q) ∈ Ω ⇒ p ≤ q, is a contractible
Banach
algebra if there is no discordant coupled of D-transitive triples of elements
of Ω.
Mathematics Subject
Classification (2000):
Primary 46H05, 46H25; Secondary 15A99
Quaestiones Mathematicae 25 (2002), 327-332
