Displaying similar documents to “On decomposition of a commutative p-normed algebra into a direct sum of ideals”

On the non-existence of norms for some algebras of functions

Bertram Yood (1994)

Studia Mathematica

Similarity:

Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for Ω = ℝ n where ℝ is the reals.

Normed "upper interval" algebras without nontrivial closed subalgebras

C. J. Read (2005)

Studia Mathematica

Similarity:

It is a long standing open problem whether there is any infinite-dimensional commutative Banach algebra without nontrivial closed ideals. This is in some sense the Banach algebraists' counterpart to the invariant subspace problem for Banach spaces. We do not here solve this famous problem, but solve a related problem, that of finding (necessarily commutative) infinite-dimensional normed algebras which do not even have nontrivial closed subalgebras. Our examples are incomplete normed...