The studing of classical, modified and weak Banach–Mazur distance, volume ratios and others asymptotic characteristics of convex bodies in many-dimensional spaces. Proof of existance of space uniformly distant from all spaces with unconditional bases. Estimate distance between the sums of normed spaces, distances from space with unconditional bases, investigation of stability extreme distant spaces at adding summand of proportional dimensionality.
Main publications:
Khrabrov A. I. Otsenki rasstoyanii mezhdu summami prostranstv $\ell^p_n$ // Vestn. S.-Peterburg. un-ta, Ser. 1. 2000. Vyp. 3 (# 17). S. 57–63.
Khrabrov A. I. Ekstremalnye ob'emnye otnosheniya dlya summ normirovannykh prostranstv // Problemy matematicheskogo analiza. Vyp. 21. Novosibirsk, Nauchnaya kniga. 2000. S. 264–275.
Khrabrov A. I. Obobschennye ob'emnye otnosheniya i rasstoyanie Banakha–Mazura // Matem. zametki. 2001. T. 70. # 6. S. 918–926.
Khrabrov A. I. Rasstoyaniya mezhdu prostranstvami s bezuslovnymi bazisami // Problemy matematicheskogo analiza. Vyp. 23. Novosibirsk, Nauchnaya kniga. 2001. S. 206–220.
