Bazı vektör-değerli Orlicz dizi uzayları üzerindeki operatörler

Abstract

Bu cal sma be s b ol umden olu smaktad r. Giri s b ol um unde; Orlicz dizi uzaylar n n geli sim s ureci ozetlendi. Ikinci b ol umde; sonraki b ol umlerde kullan lacak temel tan m, kavram, teorem ve ornekler verildi. U c unc u b ol umde; en genel vekt or de gerli dizi uzay olan s (X) tan t ld ve baz tan m ve onermeler verildi. Ayr ca, vekt or de gerli dizi uzaylar n n K othe-Toeplitz dualleri, normalli gi, monotonlu gu, perfectli gi tan t ld ve bunlarla ilgili onerme, teorem ve sonu clar verildi. D ord unc u b ol umde; skaler de gerli Orlicz dizi uzaylar ve vekt or de gerli Orlicz dizi uzaylar verildi ve bu uzaylar n baz ozellikleri incelendi. Son b ol umde; vekt or de gerli Orlicz dizi uzaylar uzerine baz sonu clar verildi ve bir baz ile ayn i sleve sahip bir teorem ispatland . Ayr ca, bu uzaylar uzerinde tan ml operat orleri karakterize eden onemli bir teorem ispatland ve bu teoremin sonu clar orneklerle incelendi.

This work consists of ve chapters. In the introduction, the Orlicz sequence spaces are summarized in the development process. In the second chapter, the basic de nitions, concepts, theorems and examples which will be useful in the next chapters have been given. In the third chapter, s(X) which is the most common vector-valued sequence space is introduced, and some the de nitions and propositions have been given. Further, K othe-Toeplitz duals, normality, monotony, perfectness of the vector-valued sequence spaces have been introduced and related to these propositions, theorems, and the results have been given. In the fourth chapter, the scalar-valued and vector-valued Orlicz sequence spaces Orlicz sequence spaces have been given and some properties of these spaces have been examined. In the last chapter, some results on vector-valued Orlicz sequence spaces have been given and a theorem which has the same function with a basis have been proved. In addition, a signi cant theorem which characterizes operators de ned on these spaces have been proved and the results of this theorem have been examined with examples.