Topological and algebraic genericity and spaceability for an extended chain of sequence spaces.

Autor: Axarlis, M., Deliyanni, I., Loukidou, Th., Nestoridis, V., Papanikos, K., Tziotziou, N.
Zdroj: Monatshefte für Mathematik; Mar2023, Vol. 200 Issue 3, p495-505, 11p
Abstrakt: Given a pair of topological vector spaces X , Y where X is a proper linear subspace of Y it is examined whether Y \ X is residual in Y (topological genericity), whether Y \ X contains a dense linear subspace of Y except 0 (algebraic genericity) and whether Y \ X contains a closed infinite dimensional subspace of Y except 0 (spaceability). In the present paper the spaces X and Y are either sequence spaces or spaces of analytic functions on the unit disc regarded as sequence spaces via the identification of a function with the sequence of its Taylor coefficients. For the spaces under consideration we give an affirmative answer to each of these questions providing general proofs which extend previous results. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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