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 or...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.展开更多
文摘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.
