Author(s)

Mohammad Sadegh Asgari, Seyedeh Sara Karimizad, Hamidreza Rahimi

Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran.

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.

Generalized Orthogonal Projection; Orthogonal Projection; Generalized e-Projection; e-Projection

M. Asgari, S. Karimizad and H. Rahimi, "On the Generality of Orthogonal Projections and e-Projections in Banach Algebras," Advances in Pure Mathematics, Vol. 2 No. 5, 2012, pp. 318-322. doi: 10.4236/apm.2012.25044.