Operators satisfying certain growth conditions. II
HTML articles powered by AMS MathViewer
- by B. C. Gupta PDF
- Proc. Amer. Math. Soc. 58 (1976), 148-150 Request permission
Abstract:
It is proved that the condition ${w_\rho }[{(T - zI)^{ - 1}}] = 1/d(z,\sigma (T)),{w_\rho }( \cdot )$ being the operator radius of Holbrook, implies the existence of certain eigenvalues and normal eigenvalues for a Hilbert space operator $T$. This extends known results based on a norm condition $(\rho = 1)$ and allows a similar extension of various consequences of these results.References
- 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
- John A. R. Holbrook, On the power-bounded operators of Sz.-Nagy and Foiaş, Acta Sci. Math. (Szeged) 29 (1968), 299–310. MR 239453
- J. G. Stampfli, Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 117 (1965), 469–476. MR 173161, DOI 10.1090/S0002-9947-1965-0173161-3
- J. G. Stampfli, A local spectral theory for operators. III. Resolvents, spectral sets and similarity, Trans. Amer. Math. Soc. 168 (1972), 133–151. MR 295114, DOI 10.1090/S0002-9947-1972-0295114-0 S. M. Patel, On some classes of operators associated with operator radii of Holbrook, 39th Annual Conf. of Indian Math. Soc., Jadavpur University, Jadavpur, 1973.
- S. M. Patel and B. C. Gupta, Operators satisfying certain growth conditions, Proc. Amer. Math. Soc. 53 (1975), no. 2, 341–346. MR 385617, DOI 10.1090/S0002-9939-1975-0385617-0
- S. K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970/71), 529–544. MR 279623, DOI 10.1512/iumj.1970.20.20044
- S. K. Berberian, Some conditions on an operator implying normality. II, Proc. Amer. Math. Soc. 26 (1970), 277–281. MR 265975, DOI 10.1090/S0002-9939-1970-0265975-3
- S. K. Berberian, Conditions on an operator implying $\textrm {Re}\,\sigma (T)=\sigma (\textrm {Re}\,T)$, Trans. Amer. Math. Soc. 154 (1971), 267–272. MR 270185, DOI 10.1090/S0002-9947-1971-0270185-5
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 148-150
- MSC: Primary 47A65
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417831-0
- MathSciNet review: 0417831