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A characterization of characters in complex m-pseudoconvex algebras

W. Żelazko (2005)

Banach Center Publications

In this paper we extend the characterization of characters given in [1], [2] and [8] onto m-pseudoconvex algebras. As a consequence (and a generalization) we give a characterization of continuous homomorphisms from m-pseudoconvex algebras into commutative semisimple m-pseudoconvex algebras.

A characterization of maximal regular ideals in lmc algebras

Maria Fragoulopoulou (1992)

Studia Mathematica

A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.

A note on the singular spectrum.

L. Lindeboom (Groenewald), H. Raubenheimer (1998)

Extracta Mathematicae

We compare the singular spectrum of a Banach algebra element with the usual spectrum and exponential spectrum.

A theorem of Gel'fand-Mazur type

Hung Le Pham (2009)

Studia Mathematica

Denote by any set of cardinality continuum. It is proved that a Banach algebra A with the property that for every collection a α : α A there exist α ≠ β ∈ such that a α a β A is isomorphic to i = 1 r ( [ X ] / X d i [ X ] ) E , where d , . . . , d r , and E is either X [ X ] / X d [ X ] for some d₀ ∈ ℕ or a 1-dimensional i = 1 r [ X ] / X d i [ X ] -bimodule with trivial right module action. In particular, ℂ is the unique non-zero prime Banach algebra satisfying the above condition.

Algebras of quotients with bounded evaluation of a normed semiprime algebra

M. Cabrera, Amir A. Mohammed (2003)

Studia Mathematica

We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation of the ideal...

An approach to joint spectra

Angel Martínez Meléndez, Antoni Wawrzyńczyk (1999)

Annales Polonici Mathematici

For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.

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