Kafes Normlu Riesz Cebirleri Üzerindeki Operatörler İçin Hahn-Banach Teoremi

X ve E Riesz cebirleri ve p:X →E_+ monoton bir vektör normu olsun. Böylece (X,p,E) üçlüsü kafes normlu Riesz cebiri olarak adlandırılır. Bu çalışmada, Hahn-Banach teoreminin kafes normlu Riesz cebirlerindeki operatörler için genişletilmesini vereceğiz. Fakat bu çalışmadaki genişleme diğer Hahn-Banach teoremlerinden farlı olmaktadır. Ayrıca bu genişlemenin bazı sonuçlarının olduğunu göstermeketeyiz.

Anahtar Kelimeler:

Hahn-Banach theoremi, Kafes normlu uzaylar, Riesz cebirleri, Riesz uzayı

Hahn-Banach Theorem for Operators on Lattice Normed Riesz Algebras

Let X and E be Riesz algebras and p:X →E_+ be a monotone vector norm. Then the triple (X,p,E) is called lattice normed Riesz algebra. In this paper, we prove a generalization of the extension of the Hahn-Banach theorem for operators on the lattice normed Riesz algebras, in which the extension of one-step of that is not similar to the other Hahn-Banach theorems. In addition, we give some applications and results.

Keywords:

Hahn-Banach theorem, Lattice normed space, Riesz algebra, Riesz apaces,

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