p-adic Banach Space Representations av Dubravka Ban

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This book systematically develops the theory of continuous representations on <i>p</i>-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive <i>p</i>-adic groups on <i>p</i>-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, <i>p</i>-adic measures and distributions, <i>p</i>-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on <i>p</i>-adic Banach spaces.<div><br></div><div>This monograph is intended to serve both as a reference book and as an int