Dual complementors in topological algebras

Marina Haralampidou

Banach Center Publications (2005)

  • Volume: 67, Issue: 1, page 219-233
  • ISSN: 0137-6934

Abstract

top
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 E x i and x i E , 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.

How to cite

top

Marina Haralampidou. "Dual complementors in topological algebras." Banach Center Publications 67.1 (2005): 219-233. <http://eudml.org/doc/282478>.

@article{MarinaHaralampidou2005,
abstract = {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.},
author = {Marina Haralampidou},
journal = {Banach Center Publications},
keywords = {annihilator algebra; dual algebra; -algebra; left complemented algebra; right complemented algebra; locally convex -algebra; locally -algebra; dual pair of complementors},
language = {eng},
number = {1},
pages = {219-233},
title = {Dual complementors in topological algebras},
url = {http://eudml.org/doc/282478},
volume = {67},
year = {2005},
}

TY - JOUR
AU - Marina Haralampidou
TI - Dual complementors in topological algebras
JO - Banach Center Publications
PY - 2005
VL - 67
IS - 1
SP - 219
EP - 233
AB - 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.
LA - eng
KW - annihilator algebra; dual algebra; -algebra; left complemented algebra; right complemented algebra; locally convex -algebra; locally -algebra; dual pair of complementors
UR - http://eudml.org/doc/282478
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.