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The aim of this paper is to introduce and study left and right versions of the class of generalized Drazin-Riesz invertible operators, as well as left and right versions of the class of generalized Drazin-meromorphic invertible operators.

Let R denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators. For a bounded linear operator T on a Banach space X we prove that T = T M ⊕ T N with T M ∈ R and T N quasinilpotent (nilpotent) if and only if T admits a generalized Kato decomposition (T is of Kato type) and 0 is not an interior point of the corresponding spectrum σ R (T ) = {λ ∈ C : T − λ / ∈ R}. In addition, we show that every non-isolated boundary point of the spectrum σ R (T ) belongs to the generalized Kato spectrum of T . 2010 Mathematics subject classification: 47A53, 47A10. Key words and phrases: generalized Kato decomposition, generalized Kato spectrum, upper and lower semi-Fredholm, semi-Weyl and semi-Browder operators.

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We used a GIS-based approach to examine the influence of road density and physical watershed features (watershed size, wetland cover, and bedrock type) on water quality in coastal marshes of Georgian Bay, Ontario. We created a GIS that included landscape information and water-quality data from a 9-year synoptic survey of 105 coastal marshes covering 28 quaternary watersheds. Multiple regressions and partial correlations were used to discern confounding effects of human-induced (road density) versus natural physical watershed determinants of water quality. Road density was the dominant factor influencing many water quality variables, showing positive correlations with specific conductivity (COND), total suspended solids (TSS), and inorganic suspended solids (ISS) and a negative correlation with overall Water Quality Index scores. Road density also showed positive correlations with total nitrate nitrogen (TNN) and total phosphorus (TP). By comparison, larger watershed area was the main factor leading to elevated TP concentrations. The proportion of the watershed occupied by wetlands explained the largest amount of variation in TNN concentrations (negative correlation) and was also negatively correlated with COND and positively correlated with TSS and ISS when we controlled for road density. Bedrock type did not have a significant effect in any of the models. Our findings suggest that road density is currently the overriding factor governing water quality of coastal marshes in Georgian Bay during the summer low-flow period. We recommend that natural variation in physical watershed characteristics be considered when developing water quality standards and management practices for freshwater coastal areas.