On Locally Convex Spaces Between Which All Linear Continuous Operators Are Bounded, Almost Bounded

Date

2025-1

Author

Taştüner, Emre

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In this thesis, we study locally convex spaces between which all linear continuous operators are bounded, almost bounded. Firstly, some necessary and sufficient conditions for a special lower triangular operator from a nuclear Köthe space to another special nuclear Köthe space to be linear and continuous are given, and also the upper triangular version of it is considered. Secondly, it is showed that if E and G are Fréchet spaces and F is a complete locally convex space, the existence of a continuous linear not almost bounded operator from E into F factoring through G causes the existence of a common nuclear Köthe subspace of the triple (E, G, F). In addition, it is proved that if F has the property (y), then (E, G, F) has a common nuclear Köthe quotient. Finally, if ℓ denotes a Banach sequence space with a monotone norm in which the canonical system (en) is an unconditional basis, the existence of an unbounded continuous linear operator between ℓ-Köthe spaces λℓ(A) and λℓ(C) factoring through a third ℓ-Köthe space λℓ(B) causes the existence of an unbounded continuous quasidiagonal operator from λℓ(A) into λℓ(C) factoring through λℓ(B) as a product of two continuous quaisdiagonal operators. Using this, it is studied when (λℓ(A), λℓ(B), λℓ(C)) satisfies the bounded factorization property, which means that all continuous linear operators from λℓ(A) into λℓ(C) factoring thorugh λℓ(B) are bounded. Moreover, for a triple of ℓ-Köthe spaces, the existence of a common basic subspace at least for two of the spaces under some conditions is studied.

Subject Keywords

Locally Convex Spaces, Unbounded Operators, Not Almost Bounded Operators, Köthe Spaces, Bounded Factorization Property

URI

https://hdl.handle.net/11511/113430

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Graduate School of Natural and Applied Sciences, Thesis