A New Closed Graph Theorem on Product Spaces
DOI:
https://doi.org/10.4067/S071609172015000400008Keywords:
Closed graph theorem, Product spaces, Bilinear map pings, Bimappings, Multimappings.Abstract
We obtain a new version of closed graph theorem on product spaces. Fernandez’s closed graph theorem for bilinear and multilinear mappings follows as a special case.References
[1] S. Banach, Theorie des Operations Lineaires, Warszawa, (1932).
[2] V. Brattka and G. Gherardi, Effective choice and boundedness principles in computable analysis, Bull. Symb. Log. 17, No. 1, pp. 73—117, (2011).
[3] P. J. Cohen, A counterexample to the closed graph theorem for bilinear maps, J. Func. Anal. 16, No. 2, pp. 235—240, (1974).
[4] C. S. Fernandez, Research notes the closed graph theorem for multilinear mappings, Internat. J. Math. Math. Sci. 19, No. 2, pp. 407—408, (1996).
[5] J. C. Ferrando and L. M. S. Ruiz, On CSuslin spaces, Math. Nachr. 288, No. 89, pp. 898—904, (2015).
[6] T. Guo, On some basic theorems of continuous module homomorphisms between random normed modules, J. Funct. Space Appl. (2013), Article Number: 989102.
[7] M. D. Mabula and S. Cobzas, Zabrejko’s lemma and the fundamental principles of functional analysis in the asymmetric case, Topology Appl. 184, No. 4, pp. 1—15, (2015).
[8] M. Saheli, A. Hasankhani and A. Nazari, Some properties of fuzzy norm of linear operators, Iran. J. Fuzzy Syst. 11, No. 2, 121—139, (2014).
[9] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, New York, (1978).
[10] M. Wojtowicz and W. Sieg, Pspaces and an unconditional closed graph theorem, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. AMat. 104, No. 1, pp. 13—18, (2010).
[11] S. Zhong and R. Li, Continuity of mappings between Fréchet spaces, J. Math. Anal. Appl. 311, No. 2, pp. 736—743, (2005).
[12] S. Zhong, R. Li and S. Y. Won, An improvement of a recent closed graph theorem, Topology Appl. 155, No. 15, pp. 1726—1729, (2008).
[2] V. Brattka and G. Gherardi, Effective choice and boundedness principles in computable analysis, Bull. Symb. Log. 17, No. 1, pp. 73—117, (2011).
[3] P. J. Cohen, A counterexample to the closed graph theorem for bilinear maps, J. Func. Anal. 16, No. 2, pp. 235—240, (1974).
[4] C. S. Fernandez, Research notes the closed graph theorem for multilinear mappings, Internat. J. Math. Math. Sci. 19, No. 2, pp. 407—408, (1996).
[5] J. C. Ferrando and L. M. S. Ruiz, On CSuslin spaces, Math. Nachr. 288, No. 89, pp. 898—904, (2015).
[6] T. Guo, On some basic theorems of continuous module homomorphisms between random normed modules, J. Funct. Space Appl. (2013), Article Number: 989102.
[7] M. D. Mabula and S. Cobzas, Zabrejko’s lemma and the fundamental principles of functional analysis in the asymmetric case, Topology Appl. 184, No. 4, pp. 1—15, (2015).
[8] M. Saheli, A. Hasankhani and A. Nazari, Some properties of fuzzy norm of linear operators, Iran. J. Fuzzy Syst. 11, No. 2, 121—139, (2014).
[9] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, New York, (1978).
[10] M. Wojtowicz and W. Sieg, Pspaces and an unconditional closed graph theorem, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. AMat. 104, No. 1, pp. 13—18, (2010).
[11] S. Zhong and R. Li, Continuity of mappings between Fréchet spaces, J. Math. Anal. Appl. 311, No. 2, pp. 736—743, (2005).
[12] S. Zhong, R. Li and S. Y. Won, An improvement of a recent closed graph theorem, Topology Appl. 155, No. 15, pp. 1726—1729, (2008).
How to Cite
[1]
S. Zhong and G. Zhao, “A New Closed Graph Theorem on Product Spaces”, Proyecciones (Antofagasta, On line), vol. 34, no. 4, pp. 401411, 1.
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