Geodesic
Continuation of a~linear operator to an involution operator
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 671-676.

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A bounded linear operator $A\colon X\to X$ in a linear topological space $X$ is called a $p$-involution operator, $p\ge2$, if $A^p=I$, where $I$ is the identity operator. In this paper, we describe linear $p$-involution operators in a linear topological space over the field $\mathbb C$ and prove that linear operators can be continued to involution operators. 
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     author = {M. I. Kadets and K. \`E. Kaibkhanov},
     title = {Continuation of a~linear operator to an involution operator},
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M. I. Kadets; K. È. Kaibkhanov. Continuation of a~linear operator to an involution operator. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 671-676. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a3/

[1] Lindenstrauss J., Tzafriri L., Classical Banach Spaces. I. Sequence Spaces, Springer, Berlin, 1977