[Settfa] Tuesday 15/11, Vladimir Muller

[kubis at math.cas.cz]

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 Tuesday 15th November, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Vladimir Muller, IM CAS
 Title: Matrices of operators

 Abstract  

 Let $T$ be a linear operator on a separable infinite-dimensional Hilbert space $H$. Then $T$ allows for a variety of matrix representations $(\langle Tu_j,u_n\rangle)_{n,j=1}^\infty$ induced by the set of all orthonormal bases $(u_n)$ in $H$. We discuss the following problem:
 

 
Problem: Let $B\subset{\bf N}\times{\bf N}$ be a subset and $a_{nj}\quad(j,n)\in B$ given complex numbers. What are natural assumptions on $B$ and $a_{nj}$ to ensure that there exists an orthonormal basis $(u_n)$ such that
 
$$\langle Tu_j,u_n\rangle=a_{nj}\qquad(n,j)\in B?$$
 

 
(joint work with Yu. Tomilov)

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .