In this paper, we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions, and then investigate those conditions under which the second adjoint of a derivation into a dual Banach module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included.2000 Mathematics subject classification: 46H20, 46H25.
N-2-pyrazinyl-2-furancarboxamide (I) and N-2-pyrazinyl-2-thiophenecarboxamide (II) are compounds containing different five-membered heteroaromatic rings, furan and thiophene, respectively. They were designed and synthesized to examine the effect of an increase in aromaticity from furan to thiophene on the crystal packing. In order to explore the various features of the crystal packing motifs in more detail, single crystal X-ray diffraction, Hirshfeld surface analysis and theoretical calculations were carried out on the two compounds. The results clearly show that the heteroatom substitution of O to S in five-membered rings led to an increase in the effectiveness of π-based interactions in II, whereas hydrogen bond interactions play a more important role in the stabilization of the supramolecular architecture of I.
In this paper, the relations between the topological centers of bounded bilinear mappings and some of their higher rank adjoints are investigated. Particularly, for a Banach algebra A, some results about the Banach A−modules and Arens regularity and strong Arens irregularity of module actions will be obtained.
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