Geodesic
Almost Normed and Quasinormed Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 130-143
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The properties of various classes of almost normed spaces and the spaces of their bounded linear operators are studied. It is shown that these spaces of operators are Banach spaces under certain conditions. It is proved that a bounded linear operator can be extended, while preserving its norm, from a dense set in an almost normed space to the entire space. 
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     author = {L. D. Kudryavtsev},
     title = {Almost {Normed} and {Quasinormed} {Spaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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L. D. Kudryavtsev. Almost Normed and Quasinormed Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 130-143. http://geodesic.mathdoc.fr/item/TM_2005_248_a13/

[1] Iosida K., Funktsionalnyi analiz, Mir, M., 1967

[2] Kudryavtsev L.D., “Pochti normirovannye prostranstva funktsii s polinomialnoi asimptotikoi”, Mat. sb., 194:1 (2003), 103–120 | MR | Zbl