Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
A remark on a paper of P. B. Djakov and M. S. Ramanujan
Date
2019-01-01
Author
Uyanik, Elif
Yurdakul, Murat Hayrettin
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
191
views
0
downloads
Cite This
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 spaces, under a splitting condition, causes the existence of a common basic subspace.
Subject Keywords
Bounded operators
,
Unbounded operators
,
l-Kothe spaces
URI
https://hdl.handle.net/11511/30037
Journal
TURKISH JOURNAL OF MATHEMATICS
DOI
https://doi.org/10.3906/mat-1905-90
Collections
Graduate School of Natural and Applied Sciences, Article
Suggestions
OpenMETU
Core
Bounded factorization property for ℓ-Köthe spaces
Yurdakul, Murat Hayrettin; Taştüner, Emre (2023-01-01)
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...
A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES
Uyanik, Elif; Yurdakul, Murat Hayrettin (2019-06-01)
For a scalar sequence (theta(n))(n is an element of N), let C be the matrix defined by c(n)(k) = theta(n-k+1) if n >= k, c(n)(k) = 0 if n < k. The map between Kothe spaces lambda(A) and lambda(B) is called a Cauchy Product map if it is determined by the triangular matrix C. In this note we introduced some necessary and sufficient conditions for a Cauchy Product map on a nuclear Kothe space lambda(A) to nuclear G(1) - space lambda(B) to be linear and continuous. Its transpose is also considered.
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...
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)) ...
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
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
E. Uyanik and M. H. Yurdakul, “A remark on a paper of P. B. Djakov and M. S. Ramanujan,”
TURKISH JOURNAL OF MATHEMATICS
, pp. 2494–2498, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30037.