# Journal of Operator Theory

Volume 48, Issue 3, Supplementary 2002 pp. 585-614.

Spectra of infinite parametrized Banach complexes**Authors**: Anar Dosiyev

**Author institution:**Institute of Mathematics and Mechanics of Azerbaijan Academy of Sciences, F. Agaev 9, Baku, 370141, Azerbaijan

**Summary:**The spectral mapping theorem $\sigma ( r ( a ) ) =r ( \sigma ( a ) ) $ for Taylor and S\l odkowski spectra is proved when the operator family $a$ generates a nilpotent Lie algebra and the family of noncommuting rational functions (and its limits) $r$ generates an infinite-dimensional projective and weak quasinilpotent Banach Lie algebra.

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