Popov M. Narrow operators and geometry of spaces of measurable functions

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0506U000554

Thesis Registration Form

0506U000554.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

10-10-2006

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

3. The thesis is devoted to a study of geometric properties of r.i. function F-spaces on non-atomic measure spaces and of continuous linear operators, defi ned on these spa- ces. We expound a theory of narrow operators and pre- sent its applications to problems on generalization of the Daugavet property, on ranges of vector measures, and on iso morphic classification of subspaces of the spaces Lp. We generalize the Pitt theorem on compactness of opera- tors; investigate some properties of bases in L1. It is shown that some classical theorems are false for non- locally convex spaces.

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Files

Diss.pdf

ar.tyt..pdf

avtref.pdf

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