{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T01:07:48Z","timestamp":1783904868559,"version":"3.55.0"},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T00:00:00Z","timestamp":1561939200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In this article, using the Mizar system [5], [2], the isomorphisms from the space of multilinear operators are discussed. In the first chapter, two isomorphisms are formalized. The former isomorphism shows the correspondence between the space of multilinear operators and the space of bilinear operators.<\/jats:p>\n                  <jats:p>The latter shows the correspondence between the space of multilinear operators and the space of the composition of linear operators. In the last chapter, the above isomorphisms are extended to isometric mappings between the normed spaces. We referred to [6], [11], [9], [3], [10] in this formalization.<\/jats:p>","DOI":"10.2478\/forma-2019-0011","type":"journal-article","created":{"date-parts":[[2019,7,22]],"date-time":"2019-07-22T05:30:45Z","timestamp":1563773445000},"page":"101-106","source":"Crossref","is-referenced-by-count":0,"title":["Isomorphisms from the Space of Multilinear Operators"],"prefix":"10.2478","volume":"27","author":[{"given":"Kazuhisa","family":"Nakasho","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2019,7,20]]},"reference":[{"key":"2026071213572637973_j_forma-2019-0011_ref_001_w2aab3b7b1b1b6b1ab1ab1Aa","unstructured":"[1] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485\u2013492, 1996."},{"key":"2026071213572637973_j_forma-2019-0011_ref_002_w2aab3b7b1b1b6b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"[2] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.10.1007\/s10817-017-9440-6604425130069070","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026071213572637973_j_forma-2019-0011_ref_003_w2aab3b7b1b1b6b1ab1ab3Aa","unstructured":"[3] Nelson Dunford and Jacob T. Schwartz. Linear operators I. Interscience Publ., 1958."},{"key":"2026071213572637973_j_forma-2019-0011_ref_004_w2aab3b7b1b1b6b1ab1ab4Aa","doi-asserted-by":"crossref","unstructured":"[4] Yuichi Futa, Noboru Endou, and Yasunari Shidama. Isometric differentiable functions on real normed space. 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