[Author]
 Reinov O. I.

[Title]
 Probabilities methods in finite dimensional functional analysis

[AMS Subj-class]
 51F20 Congruence and orthogonality
 51F25 Orthogonal and unitary groups
 15A04 Linear transformations, semilinear transformations
 46B28 Spaces of operators; tensor products; approximation properties

[Abstract]
 This is a preliminary version of a textbook based on a special course
 of lectures which was given by the author on the math-mech faculty
 of the St. Petersburg State University for students of senior courses
 of the chair of mathematical analysis. The main objects under the
 investigations are the sections (by subspaces of large dimensions)
 of the central-symmetrical bounded convex bodies lying in finite dimensional
 vector spaces. The basic question, around of which constantly there are
 actions, is how close can be these sections to some ellipsoids, if
 the dimensions of the basic spaces and their subspaces are large enough?
 The textbook is intended for students of senior courses and
 for post-graduate students of mathematical specialities, but it can be
 useful also for the experts in mathematical and functional analysis
 as well as in other fields of mathematics.
 Note that this is a preliminary incomplete variant (and, surely,
 there may be 1-2 smth like mistakes in the mathematical text).

[Comments]
 AMSTeX, Russian, 93 pp.
 The paper contains pictures (in separate PCX files).

[Contact e-mail]
 orein@1146.spb.edu