Displaying similar documents to “Incomplete normed algebra norms on Banach algebras”

Minimal incomplete norms on Banach algebras

Michael Meyer (1992)

Studia Mathematica

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We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.

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

Bertram Yood (1994)

Studia Mathematica

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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.

C*-seminorms

Bertram Yood (1996)

Studia Mathematica

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A necessary and sufficient condition is given for a*-algebra with identity to have a unique maximal C*-seminorm. This generalizes the result, due to Bonsall, that a Banach *-algebra with identity has such a*-seminorm.

Local algebras and the largest spectrum finite ideal.

Antonio Fernández López, Omar Jaa (1998)

Extracta Mathematicae

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M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof...