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H 1 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.

    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).

    Codes MSC :
    47A15 - Invariant subspaces of linear operators
    47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators

    Informations sur la rencontre

    Nom du congrès : Mathematical aspects of physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints
    Organisteurs Congrès : Krejcirik, David ; Siegl, Petr
    Dates : 05/06/17 - 09/06/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1596.html

    Citation Data

    DOI : 10.24350/CIRM.V.19181203
    Cite this video as: Gallardo-Gutiérrez, Eva (2017). The invariant subspace problem: a concrete operator theory approach. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19181203
    URI : http://dx.doi.org/10.24350/CIRM.V.19181203

    Voir aussi


    1. Cowen, Carl C., & Gallardo-Gutiérrez, Eva A. (2016). An introduction to Rota's universal operators: properties, old and new examples and future issues. Concrete Operators, 3, 43-51 - http://dx.doi.org/10.1515/conop-2016-0006