Acknowledgement
The author wishes to thank the referee for a careful reading and valuable comments and suggestions for the original draft.
References
- P. Aiena, Fredholm and local spectral theory, with applications to multipliers, Kluwer Academic Publishers, Dordrecht, 2004.
- E. Albrecht and J. Eschmeier, Analytic functional models and local spectral theory, Proc. London Math. Soc. (3) 75 (1997), no. 2, 323-348. https://doi.org/10.1112/S0024611597000373
- C. Apostol, H. Bercovici, C. Foia,s, and C. Pearcy, Quasiaffine transforms of operators, Michigan Math. J. 29 (1982), no. 2, 243-255. http://projecteuclid.org/euclid.mmj/1029002677
- H. Bercovici, Operator theory and arithmetic in H∝, Mathematical Surveys and Monographs, 26, American Mathematical Society, Providence, RI, 1988. https://doi.org/10.1090/surv/026
- S. Clary, Equality of spectra of quasi-similar hyponormal operators, Proc. Amer. Math. Soc. 53 (1975), no. 1, 88-90. https://doi.org/10.2307/2040373
- I. Colojoara and C. Foias, Theory of generalized spectral operators, Gordon and Breach, Science Publishers, New York, 1968.
- R. G. Douglas, On the operator equation S*XT = X and related topics, Acta Sci. Math. (Szeged) 30 (1969), 19-32.
- B. P. Duggal, Quasi-similar p-hyponormal operators, Integral Equations Operator Theory 26 (1996), no. 3, 338-345. https://doi.org/10.1007/BF01306546
- C. Foias and C. Pearcy, On the hyperinvariant subspace problem, J. Funct. Anal. 219 (2005), no. 1, 134-142. https://doi.org/10.1016/j.jfa.2004.04.003
- P. R. Halmos, A Hilbert Space Problem Book, second edition, Graduate Texts in Mathematics, 19, Springer-Verlag, New York, 1982.
- T. B. Hoover, Quasi-similarity of operators, Illinois J. Math. 16 (1972), 678-686. http://projecteuclid.org/euclid.ijm/1256065551 https://doi.org/10.1215/ijm/1256065551
- S. Jung, E. Ko, and J. E. Lee, On scalar extensions and spectral decompositions of complex symmetric operators, J. Math. Anal. Appl. 384 (2011), no. 2, 252-260. https://doi.org/10.1016/j.jmaa.2011.05.056
- S. Jung, E. Ko, and M.-J. Lee, On operators which are power similar to hyponormal operators, Osaka J. Math. 52 (2015), no. 3, 833-847. http://projecteuclid.org/euclid.ojm/1437137620
- I. B. Jung, E. Ko, and C. Pearcy, Aluthge transforms of operators, Integral Equations Operator Theory 37 (2000), no. 4, 437-448. https://doi.org/10.1007/BF01192831
- I. B. Jung, E. Ko, and C. Pearcy, Spectral pictures of Aluthge transforms of operators, Integral Equations Operator Theory 40 (2001), no. 1, 52-60. https://doi.org/10.1007/BF01202954
- R. Lange and S. W. Wang, New approaches in spectral decomposition, Contemporary Mathematics, 128, American Mathematical Society, Providence, RI, 1992. https://doi.org/10.1090/conm/128
- K. B. Laursen and M. M. Neumann, An introduction to local spectral theory, London Mathematical Society Monographs. New Series, 20, The Clarendon Press, Oxford University Press, New York, 2000.
- B. S. Nagy and C. Foias, Injection of shifts into strict contractions, in Linear operators and approximation, II (Proc. Conf., Math. Res. Inst., Oberwolfach, 1974), 29-37. Internat. Ser. Numer. Math., 25, Birkhauser, Basel, 1974. https://doi.org/10.1007/978-3-0348-5991-2_3
- H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer-Verlag, New York, 1973.
- J. G. Stampfli, A local spectral theory for operators. V. Spectral subspaces for hyponormal operators, Trans. Amer. Math. Soc. 217 (1976), 285-296. https://doi.org/10.2307/1997571
- D. Xia, Spectral theory of hyponormal operators, Operator Theory: Advances and Applications, 10, Birkhauser Verlag, Basel, 1983. https://doi.org/10.1007/978-3-0348-5435-1