Lineability: The Search for Linearity in Mathematics

Richard M. Aron, Luis Bernal-Gonzalez, Daniel M. Pellegrino, Juan B. Seoane Sepulveda

September 1, 2017 by Chapman and Hall/CRC
Reference
ISBN 9781138894433 - CAT# K32892
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

USD$59.95

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Features

    • Presents plenty of examples that demonstrate lineability, dense-lineability, spaceability, algebrability, and strong algebrability in different areas of mathematics
    • Includes a "what one needs to know" section at the beginning of each chapter to acquaint you with the tools needed for that specific chapter
    • Provides a collection of exercises in every chapter that illustrate existing results and encourage you to prove new results
    • Incorporates assertions with their corresponding proofs and presents some improvements to the assertions

      Summary

      Renewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in Mathematics collects the main results on the conditions for the existence of large algebraic substructures. It investigates lineability issues in a variety of areas, including real and complex analysis.

      After presenting basic concepts about the existence of linear structures, the book discusses lineability properties of families of functions defined on a subset of the real line as well as the lineability of special families of holomorphic (or analytic) functions defined on some domain of the complex plane. It next focuses on spaces of sequences and spaces of integrable functions before covering the phenomenon of universality from an algebraic point of view. The authors then describe the linear structure of the set of zeros of a polynomial defined on a real or complex Banach space and explore specialized topics, such as the lineability of various families of vectors. The book concludes with an account of general techniques for discovering lineability in its diverse degrees.

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