On the extremal extensions of a non-negative Jacobi operator. (English) Zbl 1313.47065

Ananieva, Aleksandra; Goloshchapova, Nataly

Methods Funct. Anal. Topol. 19, No. 4, 310-318 (2013).

The authors consider the minimal symmetric operator corresponding to a non-negative Jacobi infinite matrix with \(p\times p\) matrix entries. A description of non-negative selfadjoint extensions is given. In particular, explicit descriptions of the Friedrichs and Krein extensions are obtained. The method is based on the description of the extremal extensions in terms of the Weyl function; see V. A. Derkach and M. M. Malamud [J. Math. Sci., New York 73, No. 2, 141–242 (1995; Zbl 0848.47004)].

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

47B36	Jacobi (tridiagonal) operators (matrices) and generalizations
47B25	Linear symmetric and selfadjoint operators (unbounded)

Keywords:

Jacobi matrix; Friedrichs extension; Krein extension; Weyl function

Citations:

Zbl 0848.47004