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**Strong algebrability and residuality on certain sets of analytic functions.**
*(English)*
Zbl 1451.46022

In this interesting paper the authors investigate the presence of algebraic structures within certain sets of analytic functions. For instance, they show that the set of analytic functions from \(\mathbb{C}^{2}\) into \(\mathbb{C}^{2}\) which are not Lorch-analytic is spaceable and strongly \(\mathfrak{c}\)-algebrable (where \(\mathfrak{c}\) denotes the cardinality of the continuum) in the space of entire functions from \(\mathbb{C}^{2}\) into \(\mathbb{C}^{2}\). They also show that this set is not residual. Similar properties are investigated for the set of functions which belong to the the disk algebra but not a Dales-Davie algebra. Some properties of lineability are also obtained.

Reviewer: Daniel Pellegrino (João Pessoa)

### MSC:

46B87 | Lineability in functional analysis |

46G20 | Infinite-dimensional holomorphy |

46J15 | Banach algebras of differentiable or analytic functions, \(H^p\)-spaces |

46J10 | Banach algebras of continuous functions, function algebras |

46T25 | Holomorphic maps in nonlinear functional analysis |

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\textit{M. L. Lourenço} and \textit{D. M. Vieira}, Rocky Mt. J. Math. 49, No. 6, 1961--1972 (2019; Zbl 1451.46022)

### References:

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