Ivashyna T. Daugavet equation and Daugavet centers

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0415U001882

Thesis Registration Form

0415U001882.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

06-04-2015

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

New notion is introduced, namely, the notion of a Daugavet center as a linear bounded operator acting between Banach spaces and satisfying the condition that the distance from this operator to any rank-1 operator is maximal. Properties of Daugavet centers, Daugavet domains and Daugavet ranges are investigated. Basic facts of the Daugavet equation theory and the theory of narrow operators defined on spaces with the Daugavet property are generalized on Daugavet centers. Large number of examples, which illustrate different features of the generalizations obtained, are given.

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Files

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dis.pdf

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