Geodesic
Measures of Noncompactness in Regular Spaces
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 780-793

Voir la notice de l'article provenant de la source Cambridge University Press

Previous results by the author on the connection between three measures of noncompactness obtained for ${{\mathcal{L}}_{p}}$ are extended to regular spaces of measurable functions. An example is given of the advantages of some cases in comparison with others. Geometric characteristics of regular spaces are determined. New theorems for $\left( k,\,\beta\right)$ -boundedness of partially additive operators are proved.
DOI : 10.4153/CMB-2014-015-4
Mots-clés : 47H08, 46E30, 47H99, 47G10, measures of non-compactness, condensing map, partially additive operator, regular space, ideal space 
Erzakova, Nina A. Measures of Noncompactness in Regular Spaces. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 780-793. doi: 10.4153/CMB-2014-015-4
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[1] [1] Akhmerov, R. R., Kamenskii, M. I., Potapov, A. S., Rodkina, A. E., and Sadovskii, B. N., Measures of noncompactness and condensing operators. Operator Theory: Advances and Applications, 55, Birkhäuser Verlag, Basel, 1992. Google Scholar

[2] [2] Ayerbe Toledano, J. M., Dominguez Benavides, T., and López Acedo, G., Measures of noncompactness in metric fixed point theory. Operator Theory: Advances and Applications, 99, Birkhäuser Verlag, Basel, 1997. Google Scholar

[3] [3] Banas, J. and Goebel, K., Measures of noncompactness in Banach spaces. Lecture Notes in Pure and Applied Mathematics, 60, Marcel Dekker, New York, 1980. Google Scholar

[4] [4] Birman, M. Sh., Vilenkin, N. Ya., Gorin, E. A., et al., Functional analysis. (Russian) Second ed., Mathematical Reference Library, Nauka, Moscow, 1972. Google Scholar

[5] [5] Erzakova, N. A., On Measures of Non-compactness in regular spaces. Z. Anal. Anwendungen 15 (1996), no. 2. 299–307. Google Scholar | DOI

[6] [6] Erzakova, N. A., Compactness in measure and a measure of noncompactness. (Russian) Siberian Math. J. 38 (1997), no. 5, 926–928. Google Scholar

[7] [7] Erzakova, N. A., Solvability of equations with partially additive operators. Funct. Anal. Appl. 44 (2010), no. 3, 216–218. Google Scholar | DOI

[8] [8] Erzakova, N. A. On measure compact operators.Russian Math. (Iz. VUZ) 55 (2011), no. 9, 37–42. Google Scholar

[9] [9] Erzakova, N. A., On locally condensing operators. Nonlinear Anal. 75 (2012), no. 8, 3552–3557. Google Scholar | DOI

[10] [10] Erzakova, N. A. , On a certain class of condensing operators in spaces of summable functions. (Russian) In: Applied numerical analysis and mathematical modeling, Akad. Nauk SSSR, Dal’nevotochn. Otdel., Vladivostok, 1989, pp. 65–72, 176. Google Scholar

[11] [11] Krasnosel'skiĭ, M. A., Zabreĭko, P. P., Pustyl’nik, E. I., and Sobolevskiĭ, P. E., Integral operators in spaces of summable functions. Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics: Analysis, Noordhoff International Publishing, Leiden, 1976. Google Scholar

[12] [12] Väth, M., Ideal spaces. Lecture Notes in Mathematics, 1664, Springer-Verlag, Berlin, 1997. Google Scholar

[13] [13] Zabreĭko, P. P., Ideal spaces of functions. I. (Russian) Vestnik Yaroslav. Univ. Vyp. 8 (1974), 12–52. Google Scholar

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