Lineability : the search for linearity in mathematics /: the search for linearity in mathematics. (2015)

• Record Type: Book
• Further Information: Note: Richard M. Aron, Luis Bernal-Gonzalez, Daniel M. Pellegrino, Juan B. Seoane Sepulveda.
• Authors: Aron, Richard M; Bernal González, Luis; Pellegrino, Daniel M; Sepulveda, Juan B. Seoane
• Contents: Preliminary Notions and Tools; Cardinal numbers; Cardinal arithmetic; Basic concepts and results of abstract and linear algebra; Residual subsets; Lineability, spaceability, algebrability, and their variants Real Analysis; What one needs to know; Weierstrass' monsters; Differentiable nowhere monotone functions; Nowhere analytic functions and annulling functions; Surjections, Darboux functions, and related properties; Other properties related to the lack of continuity; Continuous functions that attain their maximum at only one point; Peano maps and space-filling curves Complex Analysis; What one needs to know; Nonextendable holomorphic functions: genericity; Vector spaces of nonextendable functions; Nonextendability in the unit disc; Tamed entire functions; Wild behavior near the boundary; Nowhere Gevrey differentiability Sequence Spaces, Measure Theory, and Integration ; What one needs to know; Lineability and spaceability in sequence spaces; Non-contractive maps and spaceability in sequence spaces; Lineability and spaceability in Lp [0, 1]; Spaceability in Lebesgue spaces; Lineability in sets of norm attaining operators in sequence spaces; Riemann and Lebesgue integrable functions and spaceability Universality, Hypercyclicity, and Chaos; What one needs to know; Universal elements and hypercyclic vectors; Lineability and dense-lineability of families of hypercyclic vectors; Wild behavior near the boundary, universal series, and lineability; Hypercyclicity and spaceability; Algebras of hypercyclic vectors; Supercyclicity and lineability; Frequent hypercyclicity and lineability; Distributional chaos and lineability Zeros of Polynomials in Banach Spaces ; What one needs to know; Zeros of polynomials: the results Miscellaneous; Series in classical Banach spaces; Dirichlet series; Non-convergent Fourier series; Norm-attaining functionals; Annulling functions and sequences with finitely many zeros; Sierpiński-Zygmund functions; Non-Lipschitz functions with bounded gradient; The Denjoy-Clarkson property General Techniques; What one needs to know; The negative side; When lineability implies dense-lineability; General results about spaceability; An algebrability criterion; Additivity and cardinal invariants: a brief account Bibliography Index Exercises, Notes, and Remarks appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 512.5; Algebras, Linear; Algebraic spaces; Lattice theory
• Languages: English
• ISBNs: 9781482299106
• Related ISBNs: 9781482299090
• Notes: Note: Description based on CIP data; item not viewed.
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• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.