VARIOUS TOPOLOGICAL FORMS OF VON NEUMANN REGULARITY IN BANACH ALGEBRAS

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ESSLAMZADEH G.H.; SHADAB M.

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Journal: Bulletin of the Iranian Mathematical Society Year:2011 | Volume:37 | Issue:3 Page(s): 159-170

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Title

VARIOUS TOPOLOGICAL FORMS OF VON NEUMANN REGULARITY IN BANACH ALGEBRAS

Author(s)

ESSLAMZADEH G.H. | SHADAB M. | Issue Writer Certificate

Keywords

TOPOLOGICALLY VON NEUMANN REGULAR

PRINCIPALLY VON NEUMANN REGULAR

Abstract

In this article we study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras with some other known Banach algebras and with each other. In particular we show that the class of TOPOLOGICALLY VON NEUMANN REGULAR Banach algebras contains all C*-algebras, group algebras of compact abelian groups and certain weakly amenable Banach algebras while it excludes measure algebras of certain locally compact Abelian groups. Moreover we show that in a unital amenable Banach algebra principal regularity implies topological regularity. Finally we use topological regularity to obtain some information about hereditary C*-subalgebras of a given C*-algebra.

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APA: Copy

ESSLAMZADEH, G.H., & SHADAB, M.. (2011). VARIOUS TOPOLOGICAL FORMS OF VON NEUMANN REGULARITY IN BANACH ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 37(3), 159-170. SID. https://sid.ir/paper/572198/en

Vancouver: Copy

ESSLAMZADEH G.H., SHADAB M.. VARIOUS TOPOLOGICAL FORMS OF VON NEUMANN REGULARITY IN BANACH ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2011;37(3):159-170. Available from: https://sid.ir/paper/572198/en

IEEE: Copy

G.H. ESSLAMZADEH, and M. SHADAB, “VARIOUS TOPOLOGICAL FORMS OF VON NEUMANN REGULARITY IN BANACH ALGEBRAS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 37, no. 3, pp. 159–170, 2011, [Online]. Available: https://sid.ir/paper/572198/en

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