## Undergraduate Math Union Summer Seminar Series

### On some Classes of Linear Operators in Banach Spaces

by Liudmyla Kadets | Kharkiv National V.N. Karazin University
Time: 12:30  (Thursday, Aug. 05, 2010)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
$X$ is a Banach Space, $G_1=\left\{T\in L(X):dim(T(X))\leq1\right\}$. $G_2$ is a class of linear continuous operators in $X$: $G_2=\left\{{\sum_{k=1}^\infty T_k:T_k \in G_1 \wedge \forall x\in X \sum_{k=1}^\infty \left\| T_k(x) \right\|\leq\infty}\right\}$, where the sum $\sum_{k=1}^\infty T_k$ we understand as a linear continuous operator $T$, that operate by the rule: $T(x)=\lim_{n\rightarrow\infty}\sum_{k=1}^n T_k(x)$. In the same way we build the sequence of classes $G_n=\left\{{\sum_{k=1}^\infty T_k:T_k \in G_{n-1} \wedge \forall x\in X \sum_{k=1}^\infty \left\| T_k(x) \right\|\leq\infty}\right\}$,. In the talk we discuss the question about existence of number $n$, such $G_n=L(X)$ for different spaces $X$.

#### Dates in this series

· Thursday, May. 27, 2010: Inequalities - Deck Transformations and Fundamental Groups (Will Pazner)
· Thursday, Jun. 03, 2010: Resolution of Singularities (Sergio da Silva)
· Thursday, Jun. 10, 2010: Geometric functions in one complex variable (Jonguk Yang)
· Thursday, Jun. 17, 2010: Epitaxial growth of solid thin films (Sergei Sagatov)
· Thursday, Jul. 15, 2010: On Rearrangement Inequalities (Mustazee Rahman)
· Thursday, Jul. 22, 2010: On Positivity of Steady States of the Thin Films Equation (Dan Ginsberg)
· Thursday, Jul. 29, 2010: Discrete Random Walks and Ito's Formula (Cameron Davidson-Pilon)
· Thursday, Aug. 05, 2010: On some Classes of Linear Operators in Banach Spaces (Liudmyla Kadets)
· Thursday, Aug. 12, 2010: On Set Theory, Logic, and Topological Games (Peter Burton)
· Thursday, Aug. 19, 2010: A Winning Strategy for Tic-Tac-Toe on an Affine Plane of Order 4 (Matthew Conlen and Juraj Milcak)