Isomorphism between Spaces of Multilinear Maps and Nested Compositions over Real Normed Vector Spaces

[1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-817. Open DOISearch in Google Scholar

[2] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.604425130069070 Open DOISearch in Google Scholar

[3] Yuichi Futa, Noboru Endou, and Yasunari Shidama. Isometric di erentiable functions on real normed space. Formalized Mathematics, 21(4):249–260, 2013. doi:10.2478/forma-2013-0027. Open DOISearch in Google Scholar

[4] Miyadera Isao. Functional Analysis. Riko-Gaku-Sya, 1972. Search in Google Scholar

[5] Kazuhisa Nakasho. Multilinear operator and its basic properties. Formalized Mathematics, 27(1):35–45, 2019. doi:10.2478/forma-2019-0004. Open DOISearch in Google Scholar

[6] Karol Pąk. Continuity of barycentric coordinates in Euclidean topological spaces. Formalized Mathematics, 19(3):139–144, 2011. doi:10.2478/v10037-011-0022-5. Open DOISearch in Google Scholar

[7] Marco Riccardi. Pocklington’s theorem and Bertrand’s postulate. Formalized Mathematics, 14(2):47–52, 2006. doi:10.2478/v10037-006-0007-y. Open DOISearch in Google Scholar

[8] Laurent Schwartz. Théorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997. Search in Google Scholar

[9] Laurent Schwartz. Calcul différentiel, tome 2. Analyse. Hermann, 1997. Search in Google Scholar

[10] Yasunari Shidama. The Banach algebra of bounded linear operators. Formalized Mathematics, 12(2):103–108, 2004. Search in Google Scholar

[11] Kôsaku Yosida. Functional Analysis. Springer, 1980. Search in Google Scholar