Kadets V. Banach spaces with the Daugavet property and Banach spaces with numerical index 1

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0514U000524

Thesis Registration Form

0514U000524.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

10-09-2014

Specialized Academic Board

Д 64.175.01

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Essay

We develop the theory of Banach spaces with the Daugavet property (DPr) and narrow operators. We develop theories of lush spaces and SCD sets, SCD spaces, and SCD-operators as effective tools for study of Banach spaces with numerical index 1 and of operators that satisfy the Daugavet equation or the alternative Daugavet equation. We show that a space with the DPr does not embed in a space with an unconditional basis. A negative solution of the famous problem of coincidence of numerical indices of the original space and of its dual is given.

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Files

aref.pdf

dis.pdf

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