In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain the following non-commutative analog of a result of Kaplansky. A bounded operator T on a Banach space X whose point spectrum ?p(T) contains a nonzero complex number, is weakly regular.
Esslamzadeh,G . (2011). Strong Topological Regularity and Weak Regularity of Banach Algebras. Journal of Sciences, Islamic Republic of Iran, 22(1), 71-144.
MLA
Esslamzadeh,G . "Strong Topological Regularity and Weak Regularity of Banach Algebras", Journal of Sciences, Islamic Republic of Iran, 22, 1, 2011, 71-144.
HARVARD
Esslamzadeh G. (2011). 'Strong Topological Regularity and Weak Regularity of Banach Algebras', Journal of Sciences, Islamic Republic of Iran, 22(1), pp. 71-144.
CHICAGO
G Esslamzadeh, "Strong Topological Regularity and Weak Regularity of Banach Algebras," Journal of Sciences, Islamic Republic of Iran, 22 1 (2011): 71-144,
VANCOUVER
Esslamzadeh G. Strong Topological Regularity and Weak Regularity of Banach Algebras. J. Sci. I. R. I.. 2011;22(1):71-144.
Journal of Sciences, Islamic Republic of Iran