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Displaying 81 – 100 of 142

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On locally pseudoconvexes square algebras.

Jorma Arhippainen (1995)

Publicacions Matemàtiques

Let A be an algebra over the field of complex numbers with a (Hausdorff) topology given by a family Q = {qλ|λ ∈ Λ} of square preserving rλ-homogeneous seminorms (rλ ∈ (0, 1]). We shall show that (A, T(Q)) is a locally m-convex algebra. Furthermore we shall show that A is commutative.

On the ideal structure of algebras of LMC-algebra valued functions

Jorma Arhippainen (1992)

Studia Mathematica

Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.

On the joint spectral radius

Vladimír Müller (1997)

Annales Polonici Mathematici

We prove the p -spectral radius formula for n-tuples of commuting Banach algebra elements

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

Bertram Yood (1994)

Studia Mathematica

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 = n where ℝ is the reals.

On the uniqueness of uniform norms and C*-norms

P. A. Dabhi, H. V. Dedania (2009)

Studia Mathematica

We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm; this is...

Currently displaying 81 – 100 of 142