Abstract
We prove that an infinite-dimensional Banach spaceX contains a nontrivial closedR-linealX 0 invariant both under the action of a compact additive operatorA and under the action of all continuous additive operatorsT inX suchthatT=T 1+T 2, whereT 1 A=AT 1 andT 2 A=−AT 2. IfA is a linear or antilinear compact operator, thenX 0 is a subspace ofX.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 611–615, May, 1995.
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Godich, V.I. InvariantR-lineals of some continuous additive operators. Ukr Math J 47, 707–712 (1995). https://doi.org/10.1007/BF01059044
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DOI: https://doi.org/10.1007/BF01059044