Rank one elements in Banach algebras

Από το τεύχος 43 του περιοδικού Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The aim of the present paper is to compare the two definitions of rank one elements of A banach algebra A given by P. Nylen and L. Rodman (based on the first property that rank one operators must satisfy) and by J. Erdos, S. Giotopoulos and N. Katseli (based on the second property that rank one operators must satisfy). According to author's approach the previous definitions are equivalent in the case that A is a semi-prime complex Banach algebra. (The original result is given in Theorem 2.1).

Σελ. 1

Σελ. 2

Σελ. 3

Σελ. 4

Σελ. 5