Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 4, Number 2 (2010), 11-36.
On a J-polar decomposition of a bounded operator and matrices of J-symmetric and J-skew-symmetric operators
In this paper we study a possibility of a decomposition of a bounded operator in a Hilbert space $H$ as a product of a J-unitary and a J-self-adjoint operators, where J is a conjugation (an antilinear involution). This decomposition shows an inner structure of a bounded operator in a Hilbert space. Some decompositions of J-unitary and unitary operators which generalize decompositions in the finite-dimensional case are also obtained. Matrix representations for J-symmetric and J-skew-symmetric operators are studied. Simple basic properties of J-symmetric, J-skew-symmetric and J-isometric operators are obtained.
Banach J. Math. Anal. Volume 4, Number 2 (2010), 11-36.
First available in Project Euclid: 7 February 2011
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47B99: None of the above, but in this section
Secondary: 33C05: Classical hypergeometric functions, $_2F_1$
Zagorodnyuk, Sergey M. On a J-polar decomposition of a bounded operator and matrices of J-symmetric and J-skew-symmetric operators. Banach J. Math. Anal. 4 (2010), no. 2, 11--36. doi:10.15352/bjma/1297117238. https://projecteuclid.org/euclid.bjma/1297117238