TITLE:
On the Generality of Orthogonal Projections and e-Projections in Banach Algebras
AUTHORS:
Mohammad Sadegh Asgari, Seyedeh Sara Karimizad, Hamidreza Rahimi
KEYWORDS:
Generalized Orthogonal Projection; Orthogonal Projection; Generalized e-Projection; e-Projection
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.5,
September
26,
2012
ABSTRACT: In this paper we develop the orthogonal projections and e-projections in Banach algebras. We prove some necessary and sufficient conditions for them and their spectrums. We also show that the sum of two generalized orthogonal projections u and v is a generalized orthogonal projection if, uv=vu=0. Our results generalize the results obtained for bounded linear operators on Hilbert spaces.