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RIGHTNESS CONDITIONS OF QUSINORMED SPACES

Annotation

We consider the quasinormed spaces, which are defined with the help of gen-functions are considered. For these spaces we estabilish the necessary and sufficient conditions of rightness, that is of equivalence of two notions of set boundedness: in the sense of metric and in the sense of topology of vector space.

Keywords

bounded set; right quasinormed space; gen-function; Musielak-Orlicz space

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UDC

517.51

Pages

284-289

References

1. Shragin I.V. Ob ogranichennosti mnozhestv v prostranstvakh Muselyaka–Orlicha» // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2011. T. 16. Vyp. 4. S. 1227-1228. 2. Shragin I.V. On the boundedness of sets in Musielak–Orlicz spaces // Comment. Math. 2013. V. 53. № 2. P. 405-412. 3. Musielak J. Orlicz spaces and modular spaces. Berlin: Springer, 1983. 4. Iosida K. Funktsional'nyy analiz. M.: Mir, 1967. 5. Komogoroff A. Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes // Stud. Math. 1934. T.S. P. 29-33. 6. Rudin U. Funktsional'nyy analiz. M.: Mir, 1975.

Received

2015-03-03

Section of issue

Mathematics

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