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Let E be a separated, quasi-complete and barreled locally convex space. Let TΊ and T 2 be two commuting, continuous spectral operators on E. The conditions under which TΊ + T 2 and TιT 2 are spectral operators are obtained. Further, let X be a locally compact and \f\ p dμ) Dieudonne  obtained some of the properties of Ω 1 . By using his methods, we prove that the space Ω p ( = Ω P (X, μ))(l < p < ~) is a complete metrisable space and is also weakly sequentially complete. We also obtain thedoi:10.2140/pjm.1968.25.129 fatcat:x6qho6iz4re45dntnlxjad2y5i