Operators satisfying certain growth conditions
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- by S. M. Patel and B. C. Gupta
- Proc. Amer. Math. Soc. 53 (1975), 341-346
- DOI: https://doi.org/10.1090/S0002-9939-1975-0385617-0
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Abstract:
Let $T$ be an operator on a complex Hilbert space $H$. Some growth conditions on operator radius of the resolvent of $T$ are studied. Moreover, it is shown that the conjecture, due to V. Istrătescu, that for operators $T$ satisfying growth condition $({{\text {G}}_1})$ \[ \sup \limits _{||x|| = 1} \;\{ ||Tx|{|^2} - |(Tx,\;x){|^2}\} = R_T^2,\] where ${R_T}$ is the radius of the smallest circular disk containing the spectrum $\sigma (T)$, turns out to be false.References
- Sterling K. Berberian, Approximate proper vectors, Proc. Amer. Math. Soc. 13 (1962), 111–114. MR 133690, DOI 10.1090/S0002-9939-1962-0133690-8
- William F. Donoghue Jr., On a problem of Nieminen, Inst. Hautes Études Sci. Publ. Math. 16 (1963), 31–33. MR 152892
- John A. R. Holbrook, On the power-bounded operators of Sz.-Nagy and Foiaş, Acta Sci. Math. (Szeged) 29 (1968), 299–310. MR 239453
- Vasile I. Istrăţescu, On a class of normaloid operators, Math. Z. 124 (1972), 199–202. MR 291854, DOI 10.1007/BF01110797
- Glenn R. Luecke, Topological properties of paranormal operators on Hilbert space, Trans. Amer. Math. Soc. 172 (1972), 35–43. MR 308839, DOI 10.1090/S0002-9947-1972-0308839-5
- Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR 0275190
- Toivo Nieminen, A condition for the self-adjointness of a linear operator, Ann. Acad. Sci. Fenn. Ser. A I 316 (1962), 5. MR 0139012
- George H. Orland, On a class of operators, Proc. Amer. Math. Soc. 15 (1964), 75–79. MR 157244, DOI 10.1090/S0002-9939-1964-0157244-4 S. M. Patel, On some classes of operators associated with operator radii of Holbrook, Thirty-Ninth Annual Conf. of Indian Math. Soc., Jadavpur University, Jadavpur, 1973.
- Teishirô Saitô, A theorem on boundary spectra, Acta Sci. Math. (Szeged) 33 (1972), 101–104. MR 305110
- I. H. Sheth, On a conjecture of Istrătescu, J. Indian Math. Soc. (N.S.) 38 (1974), no. 1, 2, 3, 4, 337–338 (1975). MR 402519
- J. G. Stampfli, A local spectral theory for operators, J. Functional Analysis 4 (1969), 1–10. MR 0243376, DOI 10.1016/0022-1236(69)90018-4
- C. S. Lin, On a family of generalized numerical ranges, Canadian J. Math. 26 (1974), 678–685. MR 343060, DOI 10.4153/CJM-1974-064-9
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 341-346
- MSC: Primary 47A65
- DOI: https://doi.org/10.1090/S0002-9939-1975-0385617-0
- MathSciNet review: 0385617