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On the Krull property in topological algebras

100%

Haralampidou M.

Commentationes Mathematicae

2006

tom 46

nr 2

We introduce Krull topological algebras. In particular, we characterize the Krull property in some special classes of topological algebras. Connections with the theory of semisimple annihilator $Q'$-algebras are given. Relative to this, an investigation on the relationship between Krull and (weakly) regular (viz. modular) annihilator algebras is considered. Subalgebras of certain Krull algebras are also presented. Moreover, conditions are supplied under which the Krull (resp. $Q'$-) property is preserved via algebra morphisms. As an application, we show that the quotient of a Krull $Q'$-algebra, modulo a 2-sided ideal, is a topological algebra of the same type. Finally, we study the Krull property in a certain algebra-valued function topological algebra.

Dual complementors in topological algebras

100%

Haralampidou M.

Banach Center Publications

2005

tom 67

nr 1

219-233

We deal with dual complementors on complemented topological (non-normed) algebras and give some characterizations of a dual pair of complementors for some classes of complemented topological algebras. The study of dual complementors shows their deep connection with dual algebras. In particular, we refer to Hausdorff annihilator locally C*-algebras and to proper Hausdorff orthocomplemented locally convex H*-algebras. These algebras admit, by their nature, the same type of dual pair of complementors. Dual pairs of complementors are also obtained on their closed 2-sided ideals or even on particular 1-sided ideals. If $(⊥_l,⊥_r)$ denotes a pair of complementors on a complemented algebra, then through the notion of a $⊥_l$ (resp. $⊥_r)$-projection, we get a structure theorem (analysis via minimal 1-sided ideals) for a semisimple annihilator left complemented Q'-algebra. Actually, such an algebra contains a maximal family, say $(x_i)_{i∈Λ}$, of mutually orthogonal minimal $⊥_l$-projections and the respective minimal ideals (factors of the analysis) are the $Ex_i$ and $x_iE$, i ∈ Λ. As a consequence, an analysis is given for a certain locally C*-algebra. In this case, the respective $x_i$'s are, in particular, projections in both (left and right) complementors.

Ograniczanie wyników

1 Banach Center Publications

1 Commentationes Mathematicae

2 Haralampidou M.

1 2006

1 2005

Wyniki wyszukiwania

On the Krull property in topological algebras

Dual complementors in topological algebras