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This study presents the geochemical characteristics of granitic rocks located on the northern margin of Chotanagpur Gneissic Complex (CGC), exposed in parts of Gaya district, Bihar and discusses the possible petrogenetic process and source characteristics. These granites are associated with Barabar Anorthosite Complex and Neo-proterozoic Munger-Rajgir group of rocks. The granitic litho-units identified in the field are grey, pink and porphyritic granites. On the basis of geochemical and petrographic characteristics, the grey and pink granites were grouped together as GPG while the porphyritic granites were named as PG. Both GPG and PG are enriched in SiO 2 , K 2 O, Na 2 O, REE (except Eu), Rb, Ba, HFSE (Nb, Y, Zr), depleted in MgO, CaO, Sr and are characterised by high Fe* values, Ga/Al ratios and high Zr saturation temperatures (GPG avg ∼ 861 • C and PG avg ∼ 835 • C). The REE patterns for GPG are moderately fractionated with an average (La/Yb) N ∼ 4.55 and Eu/Eu* ∼ 0.58, than PG which are strongly fractionated with an average (La/Yb) N ∼ 31.86 and Eu/Eu* ∼ 0.75. These features indicate that the granites have an A-type character. On the basis of geochemical data, we conclude that the granites are probably derived from a predominant crustal source with variable mantle involvement in a post-collisional setting.

Abstract. The paper concerns itself with the characterization of invariant subspace lattices of weighted shift operators on the Hubert space I2 with suitable conditions on their weights. This characterization is also extended to the case of Banach spaces /', 1

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