Person: GÖNÜLLÜ, UĞUR
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Dr. Öğr. Üyesi
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GÖNÜLLÜ
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UĞUR
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Publication Trace Class and Lidskiĭ trace formula in Kaplansky–Hilbert modules(2014) GÖNÜLLÜ, UĞUR; 114392In this paper, we introduce and study the concepts of the trace class op-erators and global eigenvalue of continuous Λ-linear operators in Kaplansky−Hilbertmodules. In particular, we give a variant of Lidski˘ı trace formula for cyclically com-pact operators in a Kaplansky−Hilbert modules.Publication The Rayleigh-Ritz minimax formula in Kaplansky-Hilbert modules(Springer, Van Godewijckstraat 30, 3311 Gz Dordrecht, Netherlands, 2015-06) GÖNÜLLÜ, UĞUR; 114392We give the RayleighRitz minimax formula for cyclically compact operators on KaplanskyHilbert modules.Publication Kaplansky-Hilbert modüller üzerinde tanımlı operatörlerin Schatten tipindeki sınıfları(2016) GÖNÜLLÜ, UĞUR; 114392Publication Weyl- and Horn-type inequalities for cyclically compact operators(TÜBİTAK, 2018) GÖNÜLLÜ, UĞUR; 114392A variant of Weyl- and Horn-type inequalities for cyclically compact operators on Kaplansky–Hilbert modules is given.Publication Duals of Cesaro Sequence Vector Lattices, Cesaro Sums of Banach Lattices, and Their Finite Elements(Springer Basel AG, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R.In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesaro sequence spaces ces(p) for p is an element of{0}boolean OR[1,infinity) and, second, after the Cesaro sum ces(p)(X) of a sequence of Banach spaces is introduced, where p = infinity is also allowed, we characterize their duals and the finite elements in these sums if the summed up spaces are Banach lattices. This is done by means of a remarkable extension of the corresponding result for direct sums.Publication Cyclically compact operators on Kaplansky-Hilbert modules(İstanbul Kültür Üniversitesi / Fen Bilimleri Enstitüsü / Matematik Bilgisayar Anabilim Dalı, 2014-05) GÖNÜLLÜ, UĞURThe first part of the thesis studies cyclically compact sets and operators on Kaplansky-Hilbert modules. A. G. Kusraev proved a general form of cyclically compact operators in Kaplansky-Hilbert modules using techniques of Boolean-valued analysis. We give a standart proof of this general form. Moreover, we obtain some characterizations of cyclically compact operators. The second part studies the Schatten-type classes of continuous Λ-linear operators on Kaplansky-Hilbert modules and investigates the duality of them. Furthermore, we show that the Hilbert-Schmidt class is a Kaplansky-Hilbert module. In the last part we define and study global eigenvalues of cyclically compact operators on Kaplansky-Hilbert modules and their multiplicities. We obtain Horn- and Weyl-type inequalities and Lidskiĭ trace formula for cyclically compact operators in Kaplansky-Hilbert modules.Publication Pozitif operatörler için değişmez alt-örgüler(İstanbul Kültür Üniversitesi / Fen Bilimleri Enstitüsü / Matematik Bilgisayar Anabilim Dalı, 2008-06) GÖNÜLLÜ, UĞUR; Mert ÇağlarBanach orgüleri üzerinde tanımlı bazı pozitif operatorlerin asikar olmayan kapalı degismez alt-orgülere sahip oldugu bilinmektedir. Ozel olarak her pozitif kompakt operator asikar olmayan kapalı degismez alt-orgüye sahiptir. Bu calışmada, Banach orgüleri üzerinde tanımlı, asikar olmayan kapalı degismez alt-orgülere sahip olmayan bazı pozitif operator ornekleri verilmistir. Anahtar Kelimeler: Banach Orgüsü, Pozitif Operator, Degismez Alt-orgüPublication Cesaro Vector Lattices and Their Ideals of Finite Elements(Springer, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R. R.For the Cesaro matrix C = (c(nm))(n,m?N), where c(nm) = (1)/(n), if n = m and c(nm) = 0 otherwise, the Cesaro sequence spaces ces(0), ces(p) (for 1 < p < 8) and cesoo are defined. These spaces turn out to be real vector lattices and with respect to a corresponding (naturally introduced) norm they are all Banach lattices, and so possess (or not possess) some interesting properties. In particular, the relations to their generating ideals c(0), t(p) and t(8) are investigated. Finally the ideals of all finite, totally finite and selfmajorizing elements in ces(0), ces(p) (for 1 < p <8) and ces(8) are described in detail.Publication A representation of cyclically compact operators on Kaplansky-Hilbert modules(Springer Basel Ag, Picassoplatz 4, Basel, 4052, Switzerland, 2016-01) GÖNÜLLÜ, UĞUR; 114392We give a representation of cyclically compact self-adjoint operators on Kaplansky-Hilbert modules and characterize the global eigenvalues of such operators by a sequence consisting of their global eigenvalues taken in the corresponding representation.