RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Video Library
Archive
Most viewed videos

Search
RSS
New in collection





You may need the following programs to see the files






International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin
October 9, 2018 10:30–11:20, Moscow, Steklov Mathematical Institute of RAS, Conference hall, 9th floor
 


A general property of ideals in uniform algebras

S. V. Kislyakovab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b St. Petersburg State University, Mathematics and Mechanics Faculty
Video records:
MP4 1,180.1 Mb
MP4 535.9 Mb

Number of views:
This page:108
Video files:32

S. V. Kislyakov
Photo Gallery


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: Let $I$ and $J$ be to closed ideals in a uniform algebra $A\subset C(S)$. It will be shown that if the complex conjugate $\overline{I\cap J}$ of their intersection is not included in some of them, then the sum $I+\bar{J}$ is not closed in $C(S)$.
The question arose during the joint work of the author and I. Zlotnikov on interpolation properties of coinvariant subspaces of the shift operator. The answer indicated above may be viewed as a far-reaching generalization of the fact that $C_A+\overline{C_A}\neq C(\mathbb{T})$, where $C_A$ is the disk-algebra,
$$ C_A= \{f\in C(\mathbb{T})\colon \hat{f}(n)=0\quad for\quad n<0\}. $$

The proof is based on the presence of certain very slight traces of analytic structure on an arbitrary proper uniform algebra. A similar technique was used by the author around 1987 for the proof of the Glicksberg conjecture.

Language: english

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018