Multi angle The invariant subspace problem: a concrete operator theory approach
Auteurs : Gallardo-Gutiérrez, Eva (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : 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 fifties asking, in particular, if every bounded linear operator acting on an infinite 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 difficult and indeed, it may solve the Invariant Subspace Problem.Codes MSC :
In this talk, we will focus on those concrete operators that may solve the Invariant Subspace Problem, presenting some of their main properties, exhibiting old and new examples and recent results about them obtained in collaboration with Prof. Carl Cowen (Indiana University-Purdue University).
47A15 - Invariant subspaces of linear operators
47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators