The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.
By defining folklore as artistic communication in small groups, Dan Ben-Amos led the discipline of Folklore in new directions. In Folklore Concepts, Henry Glassie and Elliott Oring have curated a selection of Ben-Amos's groundbreaking essays that explore folklore as a category in cultural communication and as a subject of scholarly research. Ben-Amos's work is well-known for sparking lively debate that often centers on why his definition intrinsically acknowledges tradition rather than expresses its connection forthright. Without tradition among people, there would be no art or communication, and tradition cannot accomplish anything on its own—only people can. Ben-Amos's focus on creative communication in communities is woven into the themes of the theoretical essays in this volume, through which he advocates for a better future for folklore scholarship. Folklore Concepts traces Ben-Amos's consistent efforts over the span of his career to review and critique the definitions, concepts, and practices of Folklore in order to build the field's intellectual history. In examining this history, Folklore Concepts answers foundational questions about what folklorists are doing, how they are doing it, and why.
The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.
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