Amenable Banach Cebirleri
Amenable Banach Cebirleri
Dosyalar
Tarih
2010-07-07
Yazarlar
Eroğlu, Didem
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Bu çalışmada, soyut harmonik analizde önemli yer tutan amenable konusu incelenmiştir. Soyut harmonik analiz, yerel kompakt gruplar ve bu gruplarla ilgili cebirleri inceler.Yerel kompakt gruplar ise reel sayıların cebirsel özellikleri (abelyen grup veya cisim) ,topolojik özellikleri (yerel kompakt ve reel sayılar üzerinde sürekli fonksiyon kavramı) ölçü özelliklerinin (integrasyon teorisinin temeli olan aralık ölçüsü) genellemesidir. Amenable kavramı yerel kompakt gruplar için çok ayırt edici özellik ve modern ölçü teorisinin kaynağıdır. Bu çalışmada da önce yarıgruplarda verilen amenable kavramının yerel kompakt gruplara genelleştirilmesi gösterilmiştir. Ölçü teorisinde, ölçünün değişmezliği ile ilgili olan amenable kavramının daha sonra Hoschchild kohomoloji terimleri ile Banach cebirlerinde nasıl tanımlandığı gösterilmiştir. Son olarak değişmeli ve değişmeli olmayan amenable radikal Banach cebirlerine örnek verilmiştir.
The subject of “amenable” which takes an important place in abstract harmonic analysis has been explored in this study. Abstract harmonic analysis deals with locally compact groups and the algebras related to these groups. Locally compact groups are the generalization of such properties of real numbers as algebraic properties (abelian group or field), topological properties (the concept of continous function on locally compact and real numbers) and measure properties (the measure of interval which is the basis of integration theory). The concept of “amenable” is the source of the very distinctive feature for locally compact groups as well as the modern measure theory. In parallel, the generalization of the amenable concept, which was first given in semigroups, to locally compact groups has been shown in this study. In measure theory, it has been shown how the amenable concept, which is related to the constancy of measure, is later defined in Hoschchild cohomology terms and in Banach algebras. Eventually, examples of commutative and non-commutative radical Banach algebras have been given.
The subject of “amenable” which takes an important place in abstract harmonic analysis has been explored in this study. Abstract harmonic analysis deals with locally compact groups and the algebras related to these groups. Locally compact groups are the generalization of such properties of real numbers as algebraic properties (abelian group or field), topological properties (the concept of continous function on locally compact and real numbers) and measure properties (the measure of interval which is the basis of integration theory). The concept of “amenable” is the source of the very distinctive feature for locally compact groups as well as the modern measure theory. In parallel, the generalization of the amenable concept, which was first given in semigroups, to locally compact groups has been shown in this study. In measure theory, it has been shown how the amenable concept, which is related to the constancy of measure, is later defined in Hoschchild cohomology terms and in Banach algebras. Eventually, examples of commutative and non-commutative radical Banach algebras have been given.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2010
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2010
Anahtar kelimeler
Jacobson radikal,
amenability,
Hoschchild kohomoloji,
Jacobson radical,
amenability,
Hoschchild cohomology