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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.

MSC:

47A15 Invariant subspaces of linear operators
47G10 Integral operators
47B38 Linear operators on function spaces (general)
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References:

[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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