[Settfa] Tuesday 05/03, Eva A. Gallardo-Gutierrez

[kubis at math.cas.cz]

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 Tuesday 5th March, 10:00am 
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 Speaker:Eva A. Gallardo-Gutierrez, Universidad Complutense de Madrid
 Title: The Invariant Subspace Problem: general operator theory vs. concrete operator theory?

 Abstract  

 The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann’s works in the ?fties asking, in particular, if every bounded linear operator acting on an in?nite dimensional separable Hilbert space has a non-trivial closed invariant subspace. Whereas there are well-known classes of bounded linear operators on Hilbert spaces that are known to have non-trivial, closed invariant subspaces (normal operators, compact operators, polynomially compact operators,...), the question of characterizing the lattice of the invariant subspaces of just a particular bounded linear operator is known to be extremely di?cult and indeed, it may solve the Invariant Subspace Problem. In this talk, we will focus on those concrete operators that may solve the Invariant Subspace Problem, presenting some of their main properties and exhibiting old and recent examples. Finally, if time permits, we will discuss about one of the main co
 unterexamples in the Banach space setting, Read’s operator, and further extensions at this regard.

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