The integration operator in two variables. (English) Zbl 0810.47004

Summary: We consider the integration operator in two variables on \(L_ 2[0,1]^ 2\), determine its multiplicity and reducing subspaces, and make some observations about its invariant and hyperinvariant subspaces.


47A15 Invariant subspaces of linear operators
47G10 Integral operators
47B38 Linear operators on function spaces (general)
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[1] Aharon Atzmon, Multilinear mappings and estimates of multiplicity, Integral Equations Operator Theory 10 (1987), no. 1, 1 – 16. · Zbl 0623.47005
[2] Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77. · Zbl 0269.47003
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