ΗΜΙΠΡΩΤΕΣ ΑΛΓΕΒΡΕΣ BANACH

THE MAIN OBJECTIVE OF THIS THESIS IS THE STUDY OF THE SEMIPRIME BANACH ALGEBRAS. MORE SPECIFICALLY THERE ARE EXAMINED PROPERTIES OF THE MINIMAL IDEALS OF SOCLE, OF THE MAXIMAL (MODULAR) IDEALS AND REPRESENTATIONS OF SEMIPRIME BANACH ALGEBRAS. THIS STUDY IS APPROACHED VIA SINGLE ELEMENTS WHICH ACT COMPACTLY. IT HAS BEEN PROVEN THAT A SEMIPRIME BANACH ALGEBRA A CONTAINS A MINIMAL IDEMPOTENT ELEMENT E (SEE MINIMAL IDEALS), IF AND ONLY IF, IT CONTAINS A SIMPLE ELEMENTS S THAT ACTS COMPACTLY AND IT DOESN'T BELONG TO RAD(A). SOC(A) IS THE SET OFTHE FINITE SUMS CONSISTED OF SINGLE ELEMENTS OF A THAT ACT COMPACTLY AND THEYDO NOT BELONG TO RAD(A). IT HAS ALSO BEEN SHOWN THAT FOR THE A THERE ARE: A BANACH SPACE E AND A CONTINUOUS EXACT REPRESENTATION Π:A -> BH(E) SUCH THAT Π(S) IS OF ORDER ONE, IF AND ONLY IF, S IS SIMPLE, ACTS COMPACTLY AND S E RAD(A).NEXT FOLLOWS A STUDY OF PROPERTIES OF THE ELEMENTS OF FINITE ORDER OF A SEMIPRIME BANACH ALGEBRAS A AND CERTAIN CONDITIONS ARE DETERMINED SUCH THAT THE ALGEBRA TO BE OF FINITE DIMENSION. BY USING THE SIMPLE ELEMENTS VARIOUS PROPERTIES OF FINITE IDEALS ARE STUDIED AS WELL AS THOSE OF MAXIMAL MODULAR IDEALS OF A MODULAR ANNIHILATOR BANACH ALGEBRA. FINALLY THEY ARE CHARACTERIZED THE SKEL1AND SKEL2 OF THE UNITY CLOSED SPHERE OF A COMMUTATIVE C*-ALGEBRAS (WITH UNITY) AND THE RELATIONSHIP OF THESE SKEL'S WITH THE SIMPLE ELEMENTS OF THE ALGEBRAARE EXAMINED.

Grantor dc:publisher

National and Kapodistrian University of Athens

Year dc:date

1986

Authors dc:creator

• Katseli, Nelli
• Κατσέλη-Τσίτσα, Νέλλη

• MODULAR ANNIHILATOR ΑΛΓΕΒΡΑ BANACH
• RADICAL ΑΛΓΕΒΡΑΣ
• ΑΠΛΟ ΣΤΟΙΧΕΙΟ
• ΕΛΑΧΙΣΤΟ ΤΑΥΤΟΔΥΝΑΜΟ
• ΗΜΙΠΡΩΤΗ ΑΛΓΕΒΡΑ BANACH
• Μαθηματικά
• ΜΕΓΙΣΤΑ MODULAR ΙΔΕΩΔΗ
• Σκελετός
• ΣΥΜΠΑΓΗΣ ΔΡΑΣΗΣ
• COMPACT ACTING
• MAXIMAL MODULAR IDEALS
• MINIMAL IDEMPOTENT
• MODULAR ANNIHILATOR BANACH ALGEBRA
• RADICAL
• SEMI-PRIME BANACH ALGEBRA
• SINGLE ELEMENT
• Skeleton
• SOCLE
• Φυσικές Επιστήμες
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/0143

OAI identifier oai:identifier

oai:10442/0143