Llavona, José G.2023-06-202023-06-2020061660-544610.1007/s00009-006-0076-8https://hdl.handle.net/20.500.14352/50053This paper is a survey of approximation results and methods by smooth functions in Banach spaces. The topics considered in the paper are the following: approximation by polynomials by C-k-functions using the method of smooth partitions of unity, approximation by the fine topology, analytic approximation and regularization in Banach spaces using the infimal convolution method.engjournal articlehttp://www.springerlink.com/content/w41221q040408316/fulltext.pdfhttp://www.springerlink.com/restricted access517.5ApproximationDifferentiabilityPolynomialsBanach-spacesDifferentiable functionsManifoldsAlgebrasAnálisis funcional y teoría de operadores