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A Riemann type theorem for unconditional convergence of operators. Proc. Amer. Math. Soc. 98 (1986), no. 3, 431–435.1088-6826 Let Kn be a sequence of bounded linear operators on a Hilbert space. The series ∑ n∈N Kn is said to converge unconditionally in the strong operator topology (SOT) if its net of finite partial sums converges in the SOT. The authors prove that if ∑ n∈N Kn is unconditionally convergent in the j=1 Kj exists in the SOT and ∑ n∈F Kn is compact for every subset F ⊂ N, then the limit lim ∑n uniform operator topology. Furthermore, if the operators Kn are all mutually diagonalizable, then the series converges absolutely uniformly

Year: 2013

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