Alpay, Safak
We discuss operators of strong type B between a Banach lattice and a Banach space and give necessary and sufficient conditions for this class of operators to coincide with weakly compact operators.


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)) ...
On L-, M-Weakly Compact and Rank-One Operators
Alpay, Safak (2013-07-26)
The finite rank, L-and M-weakly compact operators are studied. The inclusion of these classes with one another and with the weak Dunford-Pettis, almost Dunford-Pettis and b-weakly compact operators as well as the effect of these inclusions to the order structure of spaces serving as range or domain are examined.
Banach lattices on which every power-bounded operator is mean ergodic
Emelyanov, Eduard (1997-01-01)
Given a Banach lattice E that fails to be countably order complete, we construct a positive compact operator A : E --> E for which T = I - A is power-bounded and not mean ergodic. As a consequence, by using the theorem of R. Zaharopol, we obtain that if every power-bounded operator in a Banach lattice is mean ergodic then the Banach lattice is reflexive.
On bounded and unbounded operators
Uyanık, Elif; Yurdakul, Murat Hayrettin; Department of Mathematics (2017)
In this thesis we study on bounded and unbounded operators and obtain some results by considering $ell$-K"{o}the spaces. As a beginning, we introduce some necessary and sufficient conditions for a Cauchy Product map on a smooth sequence space to be continuous and linear and we consider its transpose. We use the modified version of Zahariuta's method to obtain analogous results for isomorphic classification of Cartesian products of K"{o}the spaces. We also investigate the SCBS property and show that all sepa...
Differential - Operator solutions for complex partial differential equations
Celebi, O; Sengul, S (1998-07-10)
The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.
Citation Formats
S. Alpay, “ON OPERATORS OF STRONG TYPE B,” HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, pp. 627–633, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63975.