Rabanovych V. Matrix Banach Algebras and Representation theory

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0400U001373

Thesis Registration Form

0400U001373.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

16-05-2000

Specialized Academic Board

Д.26.206.01

Essay

Matrix Banach algebras are investigated in the dissertation. It is proved that a Matrix Banach algebra of order n over a Banach k-generated algebra is generated by 3 idempotents if [n*n/2]+((-1)^n+1)/2>=k. Analogous result is valid for C*-algebras. It is shown that Matrix Banach algebra is generated by two elements if n*n+1>=k and analogous result is valid for C*-algebra. The estimetion on n and k is sharp. There are formulated conditions in term of Representattion Theory to be standard F_n-identity in an algebra. The invertibility symbols for some algebras of singular integral equations are constructed.

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