On the Generality of Orthogonal Projections and e-Projections in Banach Algebras

Mohammad Sadegh Asgari, Seyedeh Sara Karimizad, Hamidreza Rahimi

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

DOI: 10.4236/apm.2012.25044                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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