Bounded factorization property for ℓ-Köthe spaces

Date

2023-01-01

Author

Yurdakul, Murat Hayrettin
Taştüner, Emre

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

132
views

0
downloads

Let ℓ denote a Banach sequence space with a monotone norm in which the canonical system (en )n is an unconditional basis. We show that the existence of an unbounded continuous linear operator T between ℓ-Köthe spaces λℓ (A) and λℓ (C) which factors 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 quasidiagonal operators. Using this result, we study when the triple (λℓ (A), λℓ (B), λℓ (C)) satisfies the bounded factorization property BF (which means that all continuous linear operators from λℓ (A) into λℓ (C) factoring through λℓ (B) are bounded). As another application, we observe that the existence of an unbounded factorized operator for a triple of ℓ-Köthe spaces, under some additional assumptions, causes the existence of a common basic subspace at least for two of the spaces.

Subject Keywords

Bounded factorization property, Locally convex spaces, Unbounded operators, ℓ-Köthe spaces

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85149751359&origin=inward
https://hdl.handle.net/11511/102629

Journal

Filomat

DOI

https://doi.org/10.2298/fil2311631y

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Factorization of unbounded operators on Kothe spaces Terzioglou, T; Yurdakul, Murat Hayrettin; Zuhariuta, V (2004-01-01) The main result is that the existence of an unbounded continuous linear operator T between Kothe spaces lambda(A) and lambda(C) which factors through a third Kothe space A(B) causes the existence of an unbounded continuous quasidiagonal operator from lambda(A) into lambda(C) factoring through lambda(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (lambda(A), lambda(B)) ...
A remark on a paper of P. B. Djakov and M. S. Ramanujan Uyanik, Elif; Yurdakul, Murat Hayrettin (2019-01-01) Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-Kothe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Kothe matrices when every continuous linear operator between l-Kothe spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-Kothe ...
Bounded operators and complemented subspaces of Cartesian products DJAKOV, PLAMEN; TERZİOĞLU, AHMET TOSUN; Yurdakul, Murat Hayrettin; Zahariuta, V. (2011-02-01) We study the structure of complemented subspaces in Cartesian products X x Y of Kothe spaces X and Y under the assumption that every linear continuous operator from X to Y is bounded. In particular, it is proved that each non-Montel complemented subspace with absolute basis E subset of X x Y is isomorphic to a space of the form E(1) x E(2), where E(1) is a complemented subspace of X and E(2) is a complemented subspace of Y. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem Alpay, D; Kaptanoglu, HT (2000-12-15) Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier...
Frechet-Hilbert spaces and the property SCBS Uyanik, Elif; Yurdakul, Murat Hayrettin (2018-01-01) In this note, we obtain that all separable Frechet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioglu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Frechet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Frechet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Frechet-Hilbert space still takes place up to a complemented Hilbert subspace...

Citation Formats

M. H. Yurdakul and E. Taştüner, “Bounded factorization property for ℓ-Köthe spaces,” Filomat, vol. 37, no. 11, pp. 3631–3637, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85149751359&origin=inward.