### The structure of polynomial ideals in the algebra of entire functions

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A complete isomorphic classification is obtained for Köthe spaces $X=K\left(exp[\chi (p-\kappa \left(i\right))-1/p]{a}_{i}\right)$ such that $Xq{d}_{\simeq}{X}^{2}$; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and ${a}_{i}\to \infty $. Any of these spaces has the quasi-equivalence property.

New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.

We study in terms of corresponding Köthe matrices when every continuous linear operator between two Köthe spaces is bounded, the consequences of the existence of unbounded continuous linear operators, and related topics.

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