Институт математики и математического моделирования

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 13

Bahçeşehir University, Istanbul, Turkey

Analysis & PDE Center, Ghent University, Ghent, Belgium

Institute Mathematics & Math. Modeling, Almaty, Kazakhstan

“Analysis and Applied Mathematics”

Weekly Online Seminar

Date: Tuesday, May 31, 2022

Time: 14.00-15.00 (GMT+3, Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)

Zoom link: https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09,

Conference ID: 667 827 0445, Access code: 1

Speaker:

Prof. Dr. Tunç Mısırlıoğlu

Istanbul Kültür University, Istanbul, Turkey

Title: Modulus of Non-Semicompact Convexity

Abstract: The talk will consist of two parts. In the first part we develop the cornerstone the-orem given in [2, Proposition 2.1], which states that for a Banach lattice E with order contin-uous norm if D is a PL-compact subset of E then χ(D)=ρ(D), by showing that if a Banach lattice F has the positive Schur property then ρ(D)= ω(D) for any norm bounded subset D of F. Here, χ, ρ, and ω are Hausdorff measure of non-compactness, the measure of non-semicompactness introduced in [2], and the measure of weak non-compactness, respectively. Secondly, we in-troduce the notion of the modulus of non-semicompact convexity in Banach lattices defined with the help of the measure of non-semicompactness in Banach lattices. We extend the re-sults obtained in [1] by showing that the modulus of non-semicompact convexity is continu-ous and has some extra properties in reflexive Banach lattices.

References:

[1] Y. Banas, On modulus of noncompact convexity and its properties. Canad. Math. Bull., 30 (1987), 186-192.

[2] B. de Pagter & A.R. Schep, Measures of non-compactness of operators on Banach lat-tices, J. Funct. Anal., 78 (1988), 31-55.

Biography:

Tunç Mısırlıoğlu received his BSc degree from the Department of Mathematics of İs-tanbul University (İU) and his MSc degree and PhD from the Department of Mathematics of İstanbul Technical University. Before joining İstanbul Kültür University (İKU) as a fac-ulty member at the Department of Mathematics and Computer Sciences in 2009, he worked at the Department of Mathematics of İU as a faculty member for about 3 years. His research focuses on the fields of functional analysis and operator theory, Banach lattices and positive operators, invariant subspace problem, and measure of noncompactness. He has also been serving as a Director of Institute of Graduate Studies at İKU since 2017.

Forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars

Kazakh Mathematical Journal

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 13

Biography:

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