Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
14.04.1946
Keywords: indefinite metric space; extensions of symmetric operators; basicity of root vectors.
Subject:
The main object of researches is the operator theory in spaces with indefinite metrics. The invariant subspace theory for $J$-dissipative operators is developed, the basicity property for root vectors of $J$-dissipative operators is studied. There where introduced and researched special classes $(H, K(H))$ of $J$-dissipative operators and $J$-contractions, also some applications to the theory of small motions of a visco-elastic fluid are obtained. Problems in the extensions theory for isometric and symmetric operators in Krein spaces are investigated. It is obtained a representation of functions which are analytic in the origin via Krein space unitary operators.
Main publications:
Arocena R., Azizov T. Ya., Dijksma A., and Marcantognini S. A. M. On Commutant Lifting with Finite Defect. II // J. Funct. Anal., 1997, 144, no. 2, 105–116.
Azizov T. Ya., Dijksma A., Foerster K.-H., and Glaskova M. Yu. On the closedness of operator pencils // Indiana Univ. Math. J., 2000, 49, no. 1, 31–59.
Azizov T. Ya., Barsukov A. I., Dijksma A., and Jonas P. Similarity between Krein space bicontractions and Hilbert space contractions // Operator Theory: Advan. and Appl., v. 124, Birkhauser, 2001, 109–129.
