Lineability : the search for linearity in mathematics
Author(s)
Bibliographic Information
Lineability : the search for linearity in mathematics
（Monographs and research notes in mathematics）（A Chapman & Hall book）
CRC Press, c2016
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Note
Other authers: Luis Bernal González, Daniel M. Pellegrino, Juan B. Seoane Sepúlveda
Includes bibliographical references (p. 285-301) and index
Description and Table of Contents
Description
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.
Table of Contents
Preliminary Notions and Tools. Real Analysis. Complex Analysis. Sequence Spaces, Measure Theory, and Integration. Universality, Hypercyclicity, and Chaos. Zeros of Polynomials in Banach Spaces. Miscellaneous. General Techniques.
by "Nielsen BookData"