On orthogonally additive injections and surjections

• Autorzy: Baron K.

Identyfikatory

DOI

10.14708/cm.v55i2.1109

• Języki publikacji: EN

Abstrakty

EN

Let E be a real inner product space of dimension at least 2 and V a linear topological Hausdorff space. If card E≤card V, then the set of all orthogonally additive injections mapping E into V is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology. If cardV≤card E, then the set of all orthogonally additive surjections mapping E into V is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.

Słowa kluczowe

EN

orthogonal additivity; inner product space; linear topological space; Tychonoff topology; dense set

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2015
• Tom: Vol 55, No. 2
• Strony: 157--162
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Baron K.

• Institute of Mathematics University of Silesia , Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] K. Baron, On some orthogonally additive functions on inner product spaces, Ann. Univ. Sci. Budapest. Sect. Comput. 40 (2013), 123-127.
• [2] K. Baron, Orthogonally additive bijections are additive, Aequationes Math. 89 (2015), 297-299, DOI 10.1007/S00010-013-0242-6.
• [3] K. Baron, On the continuous dependence of solutions to orthogonal additivity problem on given functions, Ann. Math. Sil. 29 (2015), 19-23, DOI 10.1515/amsil-2015-0002.
• [4] K. Baron and J. Ratz, On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187-189.
• [5] M. Kuczma, An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensens inequality, 2nd ed., Birkhäuser Verlag, Basel 2009.
• [6] J. Ratz, On orthogonally additive mappings, Aequationes Math. 28 (1985), 35-49, DOI 10.1007/bf02189390.
• [7] W. Sierpiński, Cardinal and ordinal numbers, Monografie Matematyczne, vol. 34, Państwowe Wydawnictwo Naukowe, Warszawa 1958.
• [8] J. Sikorska, Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215-277, DOI 10.1007/S00010-014-0288-0.