Abstract
Hyponormality, normality and subnormality for unbounded operators on Hilbert space are investigated and quasi- similarity of such operators is discussed.
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References
G. Biriuk and E.A. Coddington, Normal extensions of unbounded formally normal operators, J. Math. Mech., 12 (1964), 617–638.
S. Clary, Equality of quasi-similar hyponomal operators, Proc. Amer. Math. Soc., 53 (1975), 88–90.
E.A. Coddington, Formally normal operators having no normal extensions, Canad. J. Math., 17 (1965), 1030–1040.
J.B. Conway, On quasisimilarity for subnormal operators, Illinois J. Math., 24 (1980), 687–702.
J.B. Conway, Subnormal operators, Pitman Adv. Pub. Program, Boston-London (1981).
R.G. Douglas, On the operator equations S*XT=X and related topics, Acta Sci. Math., 30 (1969), 19–32.
N. Dunford and J.T. Schwartz, Linear operators, Vol. II, Wiley-Interscience, New York-London-Sydney-Toronto (1971).
B. Fuglede, A commutativity problems for normal operators, Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 35–40.
P.R. Halmos, A Hilbert space problem book, Springer-Verlag, Berlin-Heidelberg-New York (1951).
T.B. Hoover, Quasi-similarity of operators, Illinois J. Math., 16 (1972), 678–686.
S. Ôta, Unbounded representations of a *-algebra on in definite metric space, preprint (1985).
C.R. Putnam, On normal operators in Hilbert space, Amer. J. Math., 73 (1951), 357–362.
C.R. Putnam, Commutation properties of Hilbert space operators and related topics, Springer-Verlag, Berlin-Heidelberg-New York (1967).
K. Schmüdgen, A formally normal operator having no normal extension, Proc. Amer. Math. Soc., 95 (1986), 503–504.
J. Stochel and F.H. Szafraniec, On normal extensions of unbounded operators I, J. Operator Theory, 14 (1985), 31–55.
J. Stochel and F.H. Szafraniec, On normal extensions of unbounded operators II, to appear in Acta Sci. Math.
M.H. Stone, Linear transformations inHilbert space and their applications to analysis, Amer. Math. Soc. Colloq. Publ., 15, Providence (1932).
B. Sz-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, American Elsevier, New York-Acad. Kidao-Budapest (1970).
J.P. Williams, Operators similar to their adjoints, Proc. Amer. Math. Soc., 20 (1969), 121–123.
J. Weidmann, Linear operators in Hilbert spaces, Springer-Verlag, Berlin-Heidelberg-New York (1980).
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Ôta, S., Schmüdgen, K. On some classes of unbounded operators. Integr equ oper theory 12, 211–226 (1989). https://doi.org/10.1007/BF01195114
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DOI: https://doi.org/10.1007/BF01195114