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On the Generality of Orthogonal Projections and e-Projections in Banach Algebras
Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran
- 1 Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran
- 2 Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran
- 3 Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Advances in Pure Mathematics·Volume 02 (2012)·Pages 318–322·Published 25 September 2012·DOI10.4236/apm.2012.25044
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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.
KeywordsGeneralized Orthogonal ProjectionOrthogonal ProjectionGeneralized e-Projectione-Projection
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