Estimates of the norm of the resolvent of a non-self-adjoint operator which is “nearly” self-adjoint or unitary

N. Dunford and J. T. Schwartz, Linear Operators. Part II, Wiley-Interscience, New York-Chichester-Brisbane-Toronto (1963).Google Scholar

I. Ts. Gokhberg and M. G. Krein, The Theory of Volterra Operators in Hilbert Space and Its Applications [in Russian], Nauka, Moscow (1967).Google Scholar

M. S. Brodskii, Triangular and Jordan Representations of Linear Operators [in Russian], Nauka, Moscow (1969).Google Scholar

M. I. Gil', “On the estimate of the norm of the resolvent operator of a completely continuous operator,” Mat. Zametki,26, No. 5, 713–717 (1979).Google Scholar

M. I. Gil', “On the estimate of the norm of a function of a Hilbert-Schmidt operator,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 14–19 (1979).Google Scholar

V. M. Brodskii and M. S. Brodskii, “On the abstract triangular representation of linear operators and the multiplicative decomposition of the characteristic functions corresponding to them,” Dokl. Akad. Nauk SSSR,181, No. 3, 511–514 (1968).Google Scholar

V. M. Brodskii, I. Ts. Gokhberg, and M. G. Krein, “General theorems on triangular representations of linear operators and multiplicative representations of their characteristic functions,” Funkts. Anal.,3, No. 4, 1–27 (1969).Google Scholar

V. M. Brodskii, “On the triangular representation of nearly unitary operators and the multiplicative decomposition of their characteristic functions,” Dokl. Akad. Nauk SSSR,190, No. 3, 510–513 (1970).Google Scholar

T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York (1976).Google Scholar