Curvature and the backward shift operators

Misra, G.

doi:10.1090/S0002-9939-1984-0735574-5

Curvature and the backward shift operators
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Proc. Amer. Math. Soc. 91 (1984), 105-107 Request permission

Abstract:

Let ${\varphi _\alpha }$ be a Möbius transformation of the unit disk ${\mathbf {D}}$, $\left | \alpha \right | < 1$. We characterize all the operators $T$ in ${B_1}\left ( {\mathbf {D}} \right )$ which are unitarily equivalent to ${\varphi _\alpha }\left ( T \right )$ for all $\alpha$ with $\left | \alpha \right | < 1$, using curvature techniques.

References

M. J. Cowen and R. G. Douglas, Complex geometry and operator theory, Acta Math. 141 (1978), no. 3-4, 187–261. MR 501368, DOI 10.1007/BF02545748
Irwin Kra, Automorphic forms and Kleinian groups, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 0357775
Gadadhar Misra, Curvature inequalities and extremal properties of bundle shifts, J. Operator Theory 11 (1984), no. 2, 305–317. MR 749164
Karim Seddighi, Essential spectra of operators in the class ${\cal B}_{n}(\Omega )$, Proc. Amer. Math. Soc. 87 (1983), no. 3, 453–458. MR 684638, DOI 10.1090/S0002-9939-1983-0684638-2
Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899