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arXiv · 1605.06251

On the existence of a factorized unbounded operator between Fréchet spaces

Ersin Kızgut·Murat Yurdakul
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Abstract

For locally convex spaces $X$ and $Y$, the continuous linear map $T:X \to Y$ is called bounded if there is a zero neighborhood $U$ of $X$ such that $T(U)$ is bounded in $Y$. Our main result is that the existence of an unbounded operator $T$ between Fréchet spaces $E$ and $F$ which factors through a third Fréchet space $G$ ends up with the fact that the triple $(E, G, F)$ has an infinite dimensional closed common nuclear Köthe subspace, provided that $F$ has the property $(y)$.

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Ersin Kızgut, Murat Yurdakul. 2016-05-20. On the existence of a factorized unbounded operator between Fréchet spaces. https://doi.org/10.1142/s1793557120500175

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