Cyclically compact operators on Kaplansky-Hilbert modules - GÖNÜLLÜ, UĞUR (İstanbul Kültür Üniversitesi / Fen Bilimleri Enstitüsü / Matematik Bilgisayar Anabilim Dalı, 2014)
The 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.
Kaplansky-Hılbert modüller üzerinde devresel kompakt operatörler
Keywords: Matematik; Mathematics