Karabyn O. Nonstandard basis in Hilbert space

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0400U002506

Thesis Registration Form

0400U002506.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

28-09-2000

Specialized Academic Board

Д 35.051.07

Ivan Franko National University of Lviv

Essay

A fragment of the nonstandard theory of bases in Hilbert space si developped. A conception of nearstandard basis and its shadow is proposed. This allows to define a criterion of nearstandardness of a vector and operator in terms of theirs corresponding coordinates and matrices. As examples, the condition of strong and uniform nearstandardness and also s-compactness of diagonal operator is obtained.

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