Some results and open questions on spaceability in function spaces
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Publication:5402103
DOI10.1090/S0002-9947-2013-05747-9zbMath1297.46022OpenAlexW2004870595MaRDI QIDQ5402103
Vladimir I. Gurariy, Per Enflo, Juan B. Seoane-Sepúlveda
Publication date: 5 March 2014
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: http://www.ams.org/journals/tran/2014-366-02/S0002-9947-2013-05747-9
Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Banach spaces of continuous, differentiable or analytic functions (46E15) Vector spaces, linear dependence, rank, lineability (15A03)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On lineability of sets of continuous functions
- Geometry of Müntz spaces and related questions
- Lineability and additivity in \(\mathbb R^{\mathbb R}\)
- Moduleability, algebraic structures, and nonlinear properties
- Lineability of the set of bounded linear non-absolutely summing operators
- A note on interpolating bases
- On the dynamics of homeomorphisms on the unit ball of \(\mathbb{R}^n\)
- Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
- Separable Banach spaces which admit \(I^ \infty_ n\) approximations
- Approximation by polynomials
- Zeros of real polynomials
- Sierpiński-Zygmund functions and other problems on lineability
- Infinite dimensional Banach spaces of functions with nonlinear properties
- Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions
- Lineability and spaceability of sets of functions on $\mathbb {R}$
- Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions
- Algebrability of the set of non-convergent Fourier series
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