Strilets' O. Algebras with additional structures and their representations

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0403U000080

Thesis Registration Form

0403U000080.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

25-12-2002

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The criteria of a hilbertian to be a left operator module over the algebra of all bounded operators on it was obtained. The linear basis of the algebra generated by finite number of idempotents, sum of which is scalar, was found. It was proved that in the case when the number of idempotents is 5 or more, such an algebra is not a PI-algebra and that the algebra generated by 4 idempotents sum of which equals 2 is a $F_4$-algebra. The necessary condition of existence of a faithful representation by unbounded operators of a *-algebra was proved. The notion of the $

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