Publication: Lineability in subsets of measure and function spaces
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2008-06
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Elsevier
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We show, among other results, that if lambda denotes the Lebesgue measure on the Borel sets in [0, 1] and X is an infinite dimensional Banach space, then the set of measures whose range is neither closed nor convex is lineable in ca(lambda, X). We also show that, in certain situations, we have lineability of the set of X-valued and non-sigma-finite measures with relatively compact range. The lineability of sets of the type L-p(I)\L-q (I) is studied and some open questions are proposed. Some classical techniques together with the converse of the Lyapunov Convexity Theorem are used.
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A. Aizpuru, C. Pérez-Eslava, J.B. Seoane-Sepúlveda, Linear structure of sets of divergent sequences and series, Linear Algebra Appl. 418 (2–3) (2006) 595–598.
R.M. Aron, D. García, M. Maestre, Linearity in non-linear problems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 95 (2001) 7–12.
R.M. Aron, V.I. Gurariy, J.B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R, Proc. Amer. Math. Soc. 133 (2005) 795–803.
R. Anantharaman, J. Diestel, Sequences in the range of a vector measure, Comment. Math. Prace Mat. 30 (2) (1991) 221–235.
R.M. Aron, D. Pérez-García, J.B. Seoane-Sepúlveda, Algebrability of the set of non-convergent Fourier series, Studia Math. 175 (2006) 83–90.
J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York, 1984.
J. Diestel, J.J. Uhl Jr., Vector measures, Mathematical Surveys, American Mathematical Society, Providence, R.I. 15 (1977).
N. Dunford, J.T. Schwartz, Linear Operators. I. General Theory, Interscience Publishers Inc., New York Interscience Publishers, Ltd., London, 1958.
P. Enflo, V.I. Gurariy, On lineability and spaceability of sets in function spaces, Preprint.
V. Fonf, V.I. Gurariy, V. Kadeˇc, An infinite dimensional subspace of C[0, 1] consisting of nowhere differentiable functions, C.R. Acad. Bulgare Sci. 52 (11–12) (1999) 13–16.
D. García, B.C. Grecu, M. Maestre, J.B. Seoane-Sepúlveda, Infinite dimensional Banach spaces of functions with nonlinear properties. Preprint.
F.J. García-Pacheco, N. Palmberg, J.B. Seoane-Sepúlveda, Lineability and algebrability of pathological phenomena in analysis, J. Math. Anal. Appl. 326 (2) (2007) 929–939.
F.J. García-Pacheco, J.B. Seoane-Sepúlveda, Vector spaces of non-measurable functions, Acta Math. Sinica (English Series) 22 (6) (2006) 1805–1808.
V.I. Gurariy, L. Quarta, On lineability of sets of continuous functions, J. Math. Anal. Appl. 294 (2004) 62–72.
S. Hencl, Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions, Proc. Amer. Math. Soc. 128 (2000) 3505–3511.
L. Janicka, N. Kalton, Vector measures of infinite variation, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (3) (1977) 239–241.
D. Puglisi, J.B. Seoane-Sepúlveda, Bounded linear non-absolutely summing operators, J. Math. Anal. Appl. 338 (2008) 292–298.
H.P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from Lp(ν) to Lr (ν), J. Funct. Anal. 4 (1969) 176–214.
E. Thomas, The Lebesgue–Nikodym theorem for vector valued measured, Mem. AMS 139 (1974).
W. Wnuk, The converse of Lyapunov convexity theorem. Comment, Math. Prace Mater. 21 (2) (1980) 389–390