Equivanishing sequences of mappings

• Autorzy: Piotr Antosik
• Języki publikacji: EN

Abstrakty

EN

Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems

Słowa kluczowe

EN

uniform strong additivity   equicontinuity   subseries convergent series  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 53
• Numer: 1
• Strony: 89-104

Daty

wydano

2000

Twórcy

autor

Piotr Antosik

• Institute of Mathematics, Polish Academy of Sciences, Katowice Branch, Bankowa 14, 40-013 Katowice, Poland

Bibliografia

• [1] P. Antosik, On the Mikusiński diagonal theorem, Bull. Acad. Polon. Sci. 19 (1971), 305-310.
• [2] P. Antosik, A diagonal theorem for nonnegative metrices and equicontinuous sequences of mappings, Bull. Acad. Polon. Sci. 24 (1976), 855-859.
• [3] P. Antosik, A lemma on matrices and its applications, Contemporary Math. 52 (1986), 89-95.
• [4] P. Antosik, J. Mikusiński and R. Sikorski, Theory of Distributions. Sequential Approach, Elsevier, Amsterdam, 1973.
• [5] P. Antosik and C. Schwartz, Matrix methods in analysis, Lecture Notes in Math. 1119, Springer, Heidelberg, 1985.
• [6] S. Banach, Théorie des opérations linéaires, Monografie Mat., vol. 1, Warszawa, 1932.
• [7] J. Distel, Sequences and series in Banach spaces, Springer Verlag, 1984.
• [8] V. M. Doubrovsky (Dubrovskii), On some properties of complete set functions and their application to a generalization of a theorem of Lebesgue, Mat. Sb. 20 (62) (1947), 317-329.
• [9] L. Drewnowski, Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym Theorems, Bull. Acad. Polon. Sci. 20 (1972), 725-731.
• [10] N. J. Kalton, Subseries convergence in topological groups and vector spaces, Israel J. Math. 10 (1971), 402-412.
• [11] C. Kliś, An example of a non-complete normed K-space, Bull. Acad. Polon. Sci. 26 (1978), 415-420.
• [12] G. Köthe, Topological vector spaces I, Springer Verlag, Berlin 1969.
• [13] I. Labuda and Z. Lipecki, On subseries convergent series and m-quasi-bases in topological spaces, Manuscr. Math. 38 (1981), 87-98.
• [14] J. Mikusiński, A theorem on vector matrices and its application in measure theory and functional analysis, Bull. Polon. Acad. Sci. 18 (1970), 193-196.
• [15] J. Mikusiński, Aksjomatyczna teoria zbieżności, preprint.
• [16] O. M. Nikodym, Sur les familles bornées de fonctions parfaitement additives d'ensembles abstraits, Monatsh. Math. Phys., 1933, 40.
• [17] W. Orlicz, Beiträge zur Theorie der Orthogonalentwicklungen II, Studia Math. 1 (1929), 241-255.
• [18] B. J. Pettis, Integration in vector spaces, Trans. Amer. Math. Soc., 44, 277-304.
• [19] C. Schwartz, Infinite matrices and the gliding hump, World Scientific, 1996.
• [20] H. Weber, Compactness in spaces of group valued contents, the Vitali-Hahn-Saks theorem and Nikodym boundedness theorem, Rocky Mt. J. Math. 16 (1986), 253-275.
• [21] A. Vilensky, Modern methods in topological vector spaces, McGraw-Hill, N.Y., 1978.