Matematik Bölümü Seminerleri "Products of Weakly Null Sequences in a Banach Algebra"
Konu : Products of Weakly Null Sequences in a Banach Algebra
Konuşmacı : Onur Oktay (Uşak Üniversitesi)
Tarih: 07.04.2021
Saat: 13:15
Yer: Seminer Zoom programı üzerinden online yapılacaktır. Katılmak isteyenlerin katılım bilgilerini alabilmeleri için huseyinuysal@istanbul.edu.tr adresine mail atmaları gerekmektedir.
Özet: Let A be a Banach algebra, (xn) and (yn) be two weakly null
sequences in A. In this talk, we are looking for an answer to the problem how
the sequences (xnyn) behave weakly. When A has a special algebra structure
(e.g., commutative C*-algebras) and/or special Banach space properties (e.g.,
Dunford-Pettis property), then one can show that (xnyn) is also weakly null.
However, this is not always the case. Surprisingly, there is no general treatment
of this problem in the literature, to the best of our knowledge. We also tie this
problem in with an unsolved conjecture: Reflexive amenable Banach algebras
are finite dimensional.
Our aim is not only to present this problem to a general audience, but also
to look for answers and constructive criticism from the experts in the field.