Compact operators with root vectors that span
HTML articles powered by AMS MathViewer
- by D. Deckard, C. Foiaş and C. Pearcy PDF
- Proc. Amer. Math. Soc. 76 (1979), 101-106 Request permission
Abstract:
A concrete example is given of a bounded, linear, compact, quasiaffinity T acting on a separable, infinite dimensional, Hilbert space $\mathcal {H}$ with the property that the eigenvectors of T span $\mathcal {H}$ but the root vectors of ${T^ \ast }$ span a subspace of $\mathcal {H}$ with infinite dimensional orthocomplement.References
- Ciprian Foiaş, Carl Pearcy, and Dan Voiculescu, The staircase representation of biquasitriangular operators, Michigan Math. J. 22 (1975), no. 4, 343–352. MR 405146
- Hans Ludwig Hamburger, Über die Zerlegung des Hilbertschen Raumes durch vollstetige lineare Transformationen, Math. Nachr. 4 (1951), 56–69 (German). MR 40587, DOI 10.1002/mana.19500040108
- A. S. Markus, A spectral synthesis problem for operators with point spectrum, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 662–688 (Russian). MR 0264436
- N. K. Nikol′skiĭ, Complete extensions of Volterra operators, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1349–1355 (Russian). MR 0336413
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 101-106
- MSC: Primary 47B05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534397-8
- MathSciNet review: 534397