Open Access

# On the extremal extensions of a non-negative Jacobi operator

### Abstract

We consider the minimal non-negative Jacobi operator with $p\times p-$matrix entries. Using the technique of boundary triplets and the corresponding Weyl functions, we describe the Friedrichs and Krein extensions of the minimal Jacobi operator. Moreover, we parametrize the set of all non-negative extensions in terms of boundary conditions.

Key words: Jacobi matrix, non-negative operator, Friedrichs and Krein extensions, boundary triplet, Weyl function.

### Article Information

 Title On the extremal extensions of a non-negative Jacobi operator Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 310-318 MathSciNet MR3156297 zbMATH 1313.47065 Milestones Received 02/04/2013; Revised 14/06/2013 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

Aleksandra Ananieva
R. Luxemburg, 74, Donetsk, 83114, Ukraine

Nataly Goloshchapova
R. Luxemburg, 74, Donetsk, 83114, Ukraine

### Citation Example

Aleksandra Ananieva and Nataly Goloshchapova, On the extremal extensions of a non-negative Jacobi operator, Methods Funct. Anal. Topology 19 (2013), no. 4, 310-318.

### BibTex

@article {MFAT690,
AUTHOR = {Ananieva, Aleksandra and Goloshchapova, Nataly},
TITLE = {On the extremal extensions of a non-negative Jacobi operator},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {4},
PAGES = {310-318},
ISSN = {1029-3531},
MRNUMBER = {MR3156297},
ZBLNUMBER = {1313.47065},
URL = {http://mfat.imath.kiev.ua/article/?id=690},
}